tkz-elements (26oct23)

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+# tkz-elements — for euclidean geometry
+
+Release 1.00b 2023/10/25
+
+## Description
+
+`tkz-elements` is the first version of a library written in lua, allowing to make all the necessary calculations to define the objects of a Euclidean geometry figure. You need to compile with `LuaLaTeX`. With `tkz-elements`, the definitions and calculations are only done with `Lua`. 
+
+ The main possibility of programmation  proposed is oriented "object programming" with object classes like point, line, triangle, circle and ellipse.  For the moment, once the calculations are done, it is `tkz-euclide` or `TikZ` which allows the drawings.
+
+## Licence
+
+This package may be modified and distributed under the terms and
+conditions of the [LaTeX Project Public License](https://www.latex-project.org/lppl/), version 1.3 or greater.
+
+
+## Requirements
+
+The package compiles with utf8 and lualatex. You need actually to load:
+
+- [tikz](https://ctan.org/pkg/tikz)
+- [tkz-euclide](https://ctan.org/pkg/tkz-euclide)
+
+## Installation
+
+The package `tkz-elements` is (will be) present in TeXLive and MiKTeX, use the package
+manager to install.
+
+You can experiment with the `tkz-elements` package by placing all of the
+distribution files in the directory containing your current tex file.
+
+The different files must be moved into the different directories in your
+installation `TDS` tree or in your `TEXMFHOME`:
+
+
+## How to use it
+
+To use the package `tkz-elements`, place the following lines in the preamble of
+your LaTeX document:
+
+```
+\usepackage{tkz-elements}
+\begin{document}
+\begin{tkzelements}
+    your code
+\end{tkzelements}
+\begin{tikzpicture}
+    your code
+\end{tikzpicture}
+```
+
+If you use the `xcolor` package, load that package before `tkz-euclide` to avoid
+package conflicts.
+
+## Documentation
+
+Documentation for `tkz-euclide` is available on `CTAN`. 
+
+## Examples
+
+All  examples given in documentation will be stored on my site : [http://altermundus.fr](http://altermundus.fr) as standalone
+files, ready for compilation. 
+
+Other examples, in French, are on my site.
+
+
+## History
+
+- First version 1.00b 
+
+## Author
+
+Alain Matthes, 5 rue de Valence, Paris 75005, al (dot) ma (at) mac (dot) com
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-circle.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-circle.tex
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+\newpage
+\section{Class circle} % (fold)
+\label{sec:class_circle}
+
+\subsection{Attributs of a circle} % (fold)
+\label{sub:attributs_of_a_circle}
+This class is also defined by two points, on the one hand the center and on the other hand a point through which the circle passes.
+
+\bgroup
+\catcode`_=12
+
+\small
+\begin{center}
+%\caption{Attributes about point circle.}
+\begin{tabular}{ll}
+\toprule
+\textbf{Attributes}     & \textbf{Application}\\
+\Iattr{circle}{center}  & |z.A = C.AB.center|\\
+\Iattr{circle}{through} & |z.B = C.AB.through|\\
+\Iattr{circle}{type}    &  |C.AB.type|   \tkzar  |C.OA.type = circle|\\
+\Iattr{circle}{radius}  &  |C.AB.radius| \tkzar   |r = C.OA.radius | $r$ real number\\
+\Iattr{circle}{north}   &  |C.AB.north|   \tkzar   |z.N = C.OA.north|\\
+\Iattr{circle}{south}   &  |C.AB.south|   \tkzar   |z.S = C.OA.south| \\
+\Iattr{circle}{east}    &  |C.AB.east|   \tkzar   |z.E = C.OA.east| \\
+\Iattr{circle}{west}    &  |C.AB.west|   \tkzar   |z.W = C.OA.west| \\
+\bottomrule %
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Example: circle attributes} % (fold)
+\label{ssub:example_circle_attributes}
+
+Three attributes are used (south, west, radius). Currently, \Igfct{package}{set\_lua\_to\_tex} (see \ref{ssub:transfer_from_lua_to_tex}) creates global macros. The |\r| macro must not already be defined.
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = .5
+   z.a   = point: new (1, 1)
+   z.b   = point: new (5, 4)
+   C.ab  = circle : new (z.a,z.b)
+   z.s   = C.ab.south
+   z.w   = C.ab.west
+   r     = C.ab.radius
+   set_lua_to_tex{"r"}
+\end{tkzelements}
+\begin{tikzpicture}
+    \tkzGetNodes
+    \tkzDrawPoints(a,b,s,w)
+    \tkzLabelPoints(a,b,s,w)
+    \tkzDrawCircle(a,b)
+    \tkzDrawSegment(a,b)
+    \tkzLabelSegment[sloped](a,b){ab = \r}
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+   scale = .5
+   z.a = point: new (1, 1)
+   z.b = point: new (5, 4)
+   C.ab = circle : new (z.a,z.b)
+   z.s = C.ab.south
+   z.w = C.ab.west
+   r   = C.ab.radius
+   set_lua_to_tex{"r"}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(a,b,s,w)
+\tkzLabelPoints(a,b,s,w)
+\tkzDrawCircle(a,b)
+\tkzDrawSegment(a,b)
+\tkzLabelSegment[sloped](a,b){ab = \r}
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+%  \caption{Class Circle}
+% subsubsection example_circle_attributes (end)
+
+% subsection attributs_of_a_circle (end)
+
+\subsection{Methods of the class circle} % (fold)
+\label{sub:methods_of_the_class_circle}
+\bgroup
+\catcode`_=12
+\small
+\begin{center}
+\begin{tabular}{ll}
+\toprule
+\textbf{Methods} & \textbf{Comments}    \\
+\midrule   \\
+\Imeth{circle}{new(O,A)} & |C.OA = circle : new (z.O,z.A)| \tkzar circle  center $O$ through $A$\\
+\midrule 
+ \textbf{Points} &\\
+\midrule 
+\Imeth{circle}{antipode (pt)} & |z.C = C.OA: antipode (z.B)| \tkzar    $[BC]$ is a dimater   \\
+\Imeth{circle}{inversion (pt)} & |z.Bp = C.AC:inversion (z.B)|\\
+\Imeth{circle}{set\_inversion (list of pts)} & |z.Bp,z.Ep,z.Cp = C.AC: set_inversion ( z.B, z.E, z.C )|\\
+\Imeth{circle}{midarc (z1,z2)} & |z.D = C.AB: midarc (z.B,z.C)| $D$ is the midarc of $\widearc{AB}$\\
+\Imeth{circle}{point (phi)} & |z.E = C.AB: point (-math.pi/3)|\\
+\Imeth{circle}{random\_pt(lower, upper)} & \\
+\Imeth{circle}{internal\_similitude (C)}  &  |z.I  = C.1 : internal_similitude (C.2)| \\
+\Imeth{circle}{external\_similitude (C)} &    |z.J  = C.1 : external_similitude (C.2)|   \\ 
+\midrule 
+ \textbf{Lines} &\\
+\midrule 
+\Imeth{circle}{radical\_axis (C)} &   \\
+\Imeth{circle}{tangent\_at (pt)} & |z.P = C.OA: tangent_at (z.M)|  $((PM) \perp (OM))$\\
+\Imeth{circle}{tangent\_from (pt)}& |z.M,z.N = C.OA: tangent_from (z.P)| \\
+\midrule 
+ \textbf{Circles} &\\
+\midrule 
+\Imeth{circle}{orthogonal\_from (pt)}  & |C= C.OA: orthogonal_from (z.P)|   \\
+\Imeth{circle}{orthogonal\_through (pta,ptb)}  & |C = C.OA: orthogonal_through (z.z1,z.z2)|\\
+\midrule 
+ \textbf{Miscellaneous} &\\
+\midrule 
+\Imeth{circle}{power (pt)}     &| p = C.OA: power (z.M)| \tkzar   power  with respect to a circle   \\
+\Imeth{circle}{in\_out (pt)} & |C.OA : in_out (z.M)| \tkzar boolean  \\
+\Imeth{circle}{draw ()} & for further use\\
+\bottomrule %
+\end{tabular}
+\end{center}
+\egroup
+% subsubsection methods_circle (end)
+
+\subsubsection{Altshiller} % (fold)
+\label{ssub:altshiller}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.P  = point : new (0,0)
+   z.Q  = point : new (5,0)
+   z.I  = point : new (3,2)
+   C.QI = circle :    new (z.Q,z.I)
+   C.PE = C.QI : orthogonal_from (z.P)
+   z.E  = C.PE.through
+   C.QE = circle :    new (z.Q,z.E)
+   _,z.F    = intersection (C.PE,C.QE)
+   z.A  = C.PE: point (math.pi/180*80)
+   L.AE = line : new (z.A,z.E)
+   _,z.C    = intersection (L.AE,C.QE)
+   L.AF = line : new (z.A,z.F)
+   L.CQ = line : new (z.C,z.Q)
+   z.D  = intersection (L.AF,L.CQ)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(P,E Q,E)
+   \tkzDrawLines[add=0 and 1](P,Q)
+   \tkzDrawLines[add=0 and 2](A,E)
+   \tkzDrawSegments(P,E E,F F,C A,F C,D)
+   \tkzDrawPoints(P,Q,E,F,A,C,D)
+   \tkzLabelPoints(P,Q,E,F,A,C,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.P  = point : new (0,0)
+z.Q  = point : new (5,0)
+z.I  = point : new (3,2)
+C.QI = circle :    new (z.Q,z.I)
+C.PE = C.QI : orthogonal_from (z.P)
+z.E  = C.PE.through
+C.QE = circle :    new (z.Q,z.E)
+_,z.F    = intersection (C.PE,C.QE)
+z.A  = C.PE: point (math.pi/180*80)
+L.AE = line : new (z.A,z.E)
+_,z.C    = intersection (L.AE,C.QE)
+L.AF = line : new (z.A,z.F)
+L.CQ = line : new (z.C,z.Q)
+z.D  = intersection (L.AF,L.CQ)
+\end{tkzelements}
+
+
+\hspace*{\fill}  
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(P,E Q,E)
+\tkzDrawLines[add=0 and 1](P,Q)
+\tkzDrawLines[add=0 and 2](A,E)
+\tkzDrawSegments(P,E E,F F,C A,F C,D)
+\tkzDrawPoints(P,Q,E,F,A,C,D)
+\tkzLabelPoints(P,Q,E,F,A,C,D)
+\end{tikzpicture}
+\hspace*{\fill}
+%subsubsection altshiller (end)
+
+\subsubsection{Lemoine} % (fold)
+\label{ssub:lemoine}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = 1.6
+   z.A   = point: new (1,0)
+   z.B   = point: new (5,2)
+   z.C   = point: new (1.2,2)
+   T     = triangle: new(z.A,z.B,z.C)
+   z.O   = T.circumcenter
+   C.OA  = circle: new (z.O,z.A)
+   L.tA  = C.OA: tangent_at (z.A)
+   L.tB  = C.OA: tangent_at (z.B)
+   L.tC  = C.OA: tangent_at (z.C)
+   z.P   = intersection (L.tA,T.bc)
+   z.Q   = intersection (L.tB,T.ac)
+   z.R   = intersection (L.tC,T.ab)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes  
+   \tkzDrawPolygon[teal](A,B,C)
+   \tkzDrawCircle(O,A)
+   \tkzDrawPoints(A,B,C,P,Q,R)
+   \tkzLabelPoints(A,B,C,P,Q,R)
+   \tkzDrawLine[blue](Q,R)
+   \tkzDrawLines[red](A,P B,Q R,C)
+   \tkzDrawSegments(A,R C,P C,Q)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 1.25
+z.A   = point: new (1,0)
+z.B   = point: new (5,2)
+z.C   = point: new (1.2,2)
+T     = triangle: new(z.A,z.B,z.C)
+z.O   = T.circumcenter
+C.OA  = circle: new (z.O,z.A)
+L.tA  = C.OA: tangent_at (z.A)
+L.tB  = C.OA: tangent_at (z.B)
+L.tC  = C.OA: tangent_at (z.C)
+z.P   = intersection (L.tA,T.bc)
+z.Q   = intersection (L.tB,T.ac)
+z.R   = intersection (L.tC,T.ab)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}[rotate=90]
+\tkzGetNodes  
+\tkzDrawPolygon[teal](A,B,C)
+\tkzDrawCircle(O,A)
+\tkzDrawPoints(A,B,C,P,Q,R)
+\tkzLabelPoints(A,B,C,P,Q,R)
+\tkzDrawLine[blue](Q,R)
+\tkzDrawLines[red](A,P B,Q R,C)
+\tkzDrawSegments(A,R C,P C,Q)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Lemoine line}
+% subsubsection lemoine (end)
+% subsection methods_of_the_class_circle (end)
+
+
+% section class_circle (end)
+\endinput
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-ellipse.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-ellipse.tex
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+\newpage
+\section{Classe ellipse} % (fold)
+\label{sec:classe_ellipse}
+
+\subsection{Attributs of an ellipse} % (fold)
+\label{sub:attributs_of_an_ellipse}
+The first attributes are the three points that define the ellipse : \Iattr{ellipse}{center} , \Iattr{ellipse}{vertex} and \Iattr{ellipse}{covertex}. The first method to define an ellipse is to give its center, then the point named \tkzname{vertex} which defines the major axis and finally the point named \tkzname{covertex} which defines the minor axis.
+
+
+\bgroup
+\catcode`_=12
+\small
+\begin{center}
+%\caption{Attributes about ellipse class.}
+\begin{tabular}{ll}
+\toprule
+\textbf{Attributes}     & \textbf{Application}\\
+\Iattr{ellipse}{center} & center of the ellipse\\
+\Iattr{ellipse}{vertex} & point of the major axis and of the ellipse\\
+\Iattr{ellipse}{covertex} & point of the minor axis and of the ellipse\\
+\Iattr{ellipse}{type}& The type is 'ellipse'\\
+\Iattr{ellipse}{Rx}& Radius from center to vertex\\
+\Iattr{ellipse}{Ry}& Radius from center to covertex\\
+\Iattr{ellipse}{slope}& Slope of the line passes through the foci\\
+\Iattr{ellipse}{Fa}& First focus\\
+\Iattr{ellipse}{Fb}& Second focus\\
+\Imeth{ellipse}{south} & See next example \ref{ssub:attributs_of_an_ellipse} \\
+\Imeth{ellipse}{north} & See next example \ref{ssub:attributs_of_an_ellipse}  \\
+\Imeth{ellipse}{west}  & See next example \ref{ssub:attributs_of_an_ellipse}  \\
+\Imeth{ellipse}{east}  & See next example \ref{ssub:attributs_of_an_ellipse}  \\
+\bottomrule %
+\end{tabular}
+\end{center}
+\egroup
+
+
+\subsubsection{Attributs of an ellipse} % (fold)
+\label{ssub:attributs_of_an_ellipse}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.C   = point: new (3 , 2)
+   z.A   = point: new (5 , 1)
+   L.CA  = line : new (z.C,z.A)
+   z.b   = L.CA.north_pa
+   L     = line : new (z.C,z.b)
+   z.B   = L : point (0.5)
+   E     = ellipse: new (z.C,z.A,z.B)
+   a     = E.Rx
+   b     = E.Ry
+   z.F1  = E.Fa
+   z.F2  = E.Fb
+   slope = math.deg(E.slope)
+   z.E   = E.east
+   z.N   = E.north
+   z.W   = E.west
+   z.S   = E.south
+   z.Co  = E.covertex
+   z.Ve  = E.vertex
+   set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \pgfkeys{/pgf/number format/.cd,fixed,precision=2}
+   \tkzGetNodes
+   \tkzDrawCircles[teal](C,A)
+   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawPoints(C,A,B,b,W,S,F1,F2)
+   \tkzLabelPoints(C,A,B)
+   \tkzDrawLine[add = .5 and .5](A,W)
+   \tkzLabelSegment[pos=1.5,above,sloped](A,W){slope = \pgfmathprintnumber{\slope}}
+   \tkzLabelPoint[below](S){South}
+   \tkzLabelPoint[below left](F1){Focus 1}
+   \tkzLabelPoint[below left](F2){Focus 2}
+   \tkzLabelPoint[above right](Ve){Vertex ; East}
+   \tkzLabelPoint[above right](Co){Covertex ; North}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.C  = point: new (3 , 2)
+z.A  = point: new (5 , 1)
+L.CA = line : new (z.C,z.A)
+z.b  = L.CA.north_pa
+L    = line : new (z.C,z.b)
+z.B  = L : point (0.5)
+E    = ellipse: new (z.C,z.A,z.B)
+a    = E.Rx
+b    = E.Ry
+z.F1 = E.Fa
+z.F2 = E.Fb
+slope    = math.deg(E.slope)
+z.E  = E.east
+z.N  = E.north
+z.W  = E.west
+z.S  = E.south
+z.Co = E.covertex
+z.Ve = E.vertex
+set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\pgfkeys{/pgf/number format/.cd,fixed,precision=2}
+\tkzGetNodes
+\tkzDrawCircles[teal](C,A)
+\tkzDrawEllipse[red](C,\a,\b,\slope)
+\tkzDrawPoints(C,A,B,b,W,S,F1,F2)
+\tkzLabelPoints(C,A,B)
+\tkzDrawLine[add = .5 and .5](A,W)
+\tkzLabelSegment[pos=1.5,above,sloped](A,W){slope = \pgfmathprintnumber{\slope}}
+\tkzLabelPoint[below](S){South}
+\tkzLabelPoint[below left](F1){Focus 1}
+\tkzLabelPoint[below left](F2){Focus 2}
+\tkzLabelPoint[above right](Ve){Vertex ; East}
+\tkzLabelPoint[above right](Co){Covertex ; North}
+\end{tikzpicture}
+\hspace*{\fill}
+% \caption{Class Ellipse}
+% subsection attributs_of_an_ellipse (end)
+
+
+\subsection{Methods of the class ellipse} % (fold)
+\label{sub:methods_of_the_class_ellipse}
+Before reviewing the methods and functions related to ellipses, let's take a look at how you can draw ellipses with \pkg{tkz-elements}. The \tkzcname{tkzDrawEllipse} macro requires 4 arguments: the center of the ellipse, the long radius (on the focus axis), the short radius and the angle formed by the focus axis.
+The last three arguments must be transferred from \tkzNameEnv{tkzelements} to \tkzNameEnv{tikzpicture}.
+To do this, you'll need to use a \pkg{tkz-elements }function: \Igfct{package}{set\_lua\_to\_tex}. See \ref{sec:math_functions} or the next examples. 
+
+\vskip 1em
+\lefthand\  You need to proceed with care, because unfortunately at the moment, the macros you create are global and you can overwrite existing macros. One solution is either to choose a macro name that won't cause any problems, or to save the initial macro.
+
+\bgroup
+\catcode`_=12 
+\small
+\begin{center}
+%\caption{elements\_ellipses.lua}
+\begin{tabular}{ll}
+\toprule
+\textbf{Methods} & \textbf{Example}     \\
+\midrule 
+\Imeth{ellipse}{new (pc, pa ,pb)  }   &  E = ellipse: new ( center, vertex, covertex )   \\
+\midrule
+\Imeth{ellipse}{foci (f1,f2,v)} &  E = ellipse: foci ( focus 1, focus 2, vertex )    \\
+\Imeth{ellipse}{radii (c,a,b,sl) }     &   E = ellipse: radii ( center, radius a, radius b, slope )  \\
+\Imeth{ellipse}{in\_out (pt) }   & pt in/out of the ellipse  \\
+\Imeth{ellipse}{tangent\_at (pt) }     &  see example \ref{ssub:method_point}   \\
+\Imeth{ellipse}{tangent\_from (pt) }    &  see example \ref{ssub:method_point}    \\
+\Imeth{ellipse}{point (phi)  }   &  vertex = point (0) covertex = point (math.pi/4) ex see  \ref{ssub:method_point}   \\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Method \Imeth{ellipse}{new}} % (fold)
+\label{ssub:method_imeth_ellipse_new}
+The main method for creating a new ellipse is \Imeth{ellipse}{new}. The arguments are three: \Iattr{ellipse}{center}, \Iattr{ellipse}{vertex} and \Iattr{ellipse}{covertex}
+For attributes see  \ref{sec:classe_ellipse}
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.C      = point: new (3 , 2)
+   z.A      = point: new (5 , 1)
+   z.B      = z.C : homothety(0.5,
+              z.C : rotation (math.pi/2,z.A))
+   E        = ellipse: new (z.C,z.A,z.B)
+   a        = E.Rx
+   b        = E.Ry
+   slope    = math.deg(E.Sl)
+   set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[teal](C,A)
+   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawPoints(C,A,B)
+   \tkzLabelPoints(C,A,B)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+z.C    = point: new (3 , 2)
+z.A    = point: new (5 , 1)
+z.B    = z.C : homothety(0.5,
+         z.C : rotation (math.pi/2,z.A))
+E     = ellipse: new (z.C,z.A,z.B)
+a     = E.Rx
+b     = E.Ry
+slope = math.deg(E.slope)
+set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[teal](C,A)
+\tkzDrawEllipse[red](C,\a,\b,\slope)
+\tkzDrawPoints(C,A,B)
+\tkzLabelPoints(C,A,B)
+\end{tikzpicture}
+\end{minipage}
+
+The function \Igfct{package}{set\_lua\_to\_tex (list)} is used to define the macros that will be used to draw the ellipse with \TIKZ\ or \pkg{tkz-euclide}.
+% subsubsection method_imeth_ellipse_new (end)
+
+
+\subsubsection{Method \Imeth{ellipse}{foci}} % (fold)
+\label{ssub:function_tkzname_ellipse__foci}
+The first two points are the foci of the ellipse. The third one is the vertex. We can deduce all the other characteristics.
+
+\emph{The function launches the |new| method, all the characteristics of the ellipse are defined.}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (5 , 1)
+   L.AB     = line : new (z.A,z.B)
+   z.C      = point: new (.8 , 3)
+   T.ABC    = triangle: new (z.A,z.B,z.C)
+   z.N      = T.ABC.eulercenter
+   z.H      = T.ABC.orthocenter
+   z.O      = T.ABC.circumcenter
+   _,_,z.Mc = get_points (T.ABC: medial ())
+   L.euler  = line: new (z.H,z.O)
+   C.circum = circle: new (z.O,z.A)
+   C.euler  = circle: new (z.N,z.Mc)
+   z.i,z.j  = intersection (L.euler,C.circum)
+   z.I,z.J  = intersection (L.euler,C.euler)
+   E        = ellipse: foci (z.H,z.O,z.I)
+   L.AH     = line: new (z.A,z.H)
+   z.X      = intersection (L.AH,C.circum)
+   L.XO     = line: new (z.X,z.O)
+   z.R,z.S  = intersection (L.XO,E)
+   a,b      = E.Rx,E.Ry
+   ang      = math.deg(E.slope)
+   set_lua_to_tex{'a','b','ang'}
+\end{tkzelements}
+\end{tkzexample}
+\begin{minipage}{0.6\textwidth}
+ \begin{tkzexample}[latex=0cm,small,code only]
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircles[cyan](O,A N,I)
+   \tkzDrawSegments(X,R A,X)
+   \tkzDrawEllipse[red](N,\a,\b,\ang)
+   \tkzDrawLines[add=.2 and .5](I,H)
+   \tkzDrawPoints(A,B,C,N,O,X,H,R,S,I)
+   \tkzLabelPoints[above](C,X)
+   \tkzLabelPoints[above right](N,O)
+   \tkzLabelPoints[above left](R)
+   \tkzLabelPoints[left](A)
+   \tkzLabelPoints[right](B,I,S,H)
+   \end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+   scale =1
+   z.A   = point: new (0 , 0)
+   z.B   = point: new (5 , 1)
+   L.AB  = line : new (z.A,z.B)
+   z.C   = point: new (.8 , 3)
+   T.ABC     = triangle: new (z.A,z.B,z.C)
+   z.N = T.ABC.eulercenter
+   z.H = T.ABC.orthocenter
+   z.O = T.ABC.circumcenter
+   _,_,z.Mc  = get_points (T.ABC: medial ())
+   L.euler   = line: new (z.H,z.O)
+   C.circum  = circle: new (z.O,z.A)
+   C.euler   = circle: new (z.N,z.Mc)
+   z.i,z.j   = intersection (L.euler,C.circum)
+   z.I,z.J   = intersection (L.euler,C.euler)
+   E     = ellipse: foci (z.H,z.O,z.I)
+   L.AH  = line: new (z.A,z.H)
+   z.X   = intersection (L.AH,C.circum)
+   L.XO  = line: new (z.X,z.O)
+   z.R,z.S   = intersection (L.XO,E)
+   a,b   = E.Rx,E.Ry
+   ang   = math.deg(E.slope)
+   set_lua_to_tex{'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircles[cyan](O,A N,I)
+\tkzDrawSegments(X,R A,X)
+\tkzDrawEllipse[red](N,\a,\b,\ang)
+\tkzDrawLines[add=.2 and .5](I,H)
+\tkzDrawPoints(A,B,C,N,O,X,H,R,S,I)
+\tkzLabelPoints[above](C,X)
+\tkzLabelPoints[above right](N,O)
+\tkzLabelPoints[above left](R)
+\tkzLabelPoints[left](A)
+\tkzLabelPoints[right](B,I,S,H)
+\end{tikzpicture}
+\end{minipage}
+% subsubsection function_tkzname_ellipse__foci (end)
+
+\subsubsection{Method \Imeth{ellipse}{point} and \Imeth{ellipse}{radii}} % (fold)
+\label{ssub:method_point}
+ The method \Imeth{ellipse}{point} defines a point $M$ of the ellipse whose coordinates are $(a\times  cos(phi), b\times sin(phi))$. |phi| angle between (center,vertex) and (center,M)
+
+ \emph{The environment \tkzNameEnv{tkzelements} uses as \tkzname{lua} the radian as unit for angles. }
+
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.C         = point: new (2 , 3)
+   z.A         = point: new (6 , 5)
+   a           = value(4)
+   b           = value(3)
+   ang         = math.deg(-math.pi/4)
+   E           = ellipse: radii (z.C,a,b,-math.pi/4)
+   z.V         = E : point (0)
+   z.K         = E : point (1)
+   z.CoV       = E : point (math.pi/2)
+   z.X         = E : point (math.pi)
+   L           = E :tangent_at (z.V)
+   z.x,z.y     = get_points(L)
+   L.ta,L.tb   = E :tangent_from (z.A)
+   z.M         = L.ta.pb
+   z.N         = L.tb.pb
+   L.K         = E :tangent_at (z.K)
+   z.ka,z.kb   = get_points(L.K)
+   set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegments(C,V C,CoV)
+   \tkzDrawLines(x,y A,M A,N ka,kb)
+   \tkzLabelSegment(C,V){$a$}
+   \tkzLabelSegment[right](C,CoV){$b$}
+   \tkzDrawEllipse[teal](C,\a,\b,\ang)
+   \tkzDrawPoints(C,V,CoV,X,x,y,M,N,A,K)
+   \tkzLabelPoints(C,V,A,M,N,K)
+   \tkzLabelPoints[above left](CoV)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+scale       = .5
+z.C         = point: new (2 , 3)
+z.A         = point: new (6 , 5)
+a           = value(4)
+b           = value(3)
+ang         = math.deg(-math.pi/4)
+E           = ellipse: radii (z.C,a,b,-math.pi/4)
+z.V         = E : point (0)
+z.K         = E : point (1)
+z.CoV       = E : point (math.pi/2)
+z.X         = E : point (math.pi)
+L           = E :tangent_at (z.V)
+z.x,z.y     = get_points(L)
+L.ta,L.tb   = E :tangent_from (z.A)
+z.M         = L.ta.pb
+z.N         = L.tb.pb
+L.K         = E :tangent_at (z.K)
+z.ka,z.kb   = get_points(L.K)
+set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawSegments(C,V C,CoV)
+\tkzDrawLines(x,y A,M A,N ka,kb)
+\tkzLabelSegment(C,V){$a$}
+\tkzLabelSegment[right](C,CoV){$b$}
+\tkzDrawEllipse[teal](C,\a,\b,\ang)
+\tkzDrawPoints(C,V,CoV,X,x,y,M,N,A,K)
+\tkzLabelPoints(C,V,A,M,N,K)
+\tkzLabelPoints[above left](CoV)
+\end{tikzpicture}
+\end{minipage}
+% subsubsection method_point (end)
+% subsection methods_of_the_class_ellipse (end)
+
+% section classe_ellipse (end)
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-line.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-line.tex
new file mode 100644
index 00000000000..de11a45a518
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-line.tex
@@ -0,0 +1,420 @@
+\newpage
+\section{Class line} % (fold)
+\label{sec:class_line}
+
+\subsection{Attributs of a line} % (fold)
+\label{sub:attributs_of_a_line}
+
+Writing |L.AB = line: new (z.A,z.B) | creates an object of the class \tkzname{line} (the notation is arbitrary for the moment). Geometrically it is as much the line passing through the points $A$ and $B$ as the segment $[AB]$. Thus we can use the midpoint of |L.AB| which is of course the midpoint of the segment $[AB]$. This medium is obtained with |L.AB.mid|. Note that |L.AB.pa = z.A| and |L.AB.pb = z.B|. Finally, if a line $L$ is the result of a method, you can obtain the points with |z.A,z.B = get_points (L)| or with the previous remark.
+
+The attributes are :
+
+\bgroup
+\catcode`_=12
+
+\small
+\begin{center}
+%\caption{Attributes  about line class.}
+\begin{tabular}{ll}
+\toprule
+\textbf{Attributes} & \textbf{Application}\\
+\Iattr{line}{pa}  & First point of the segment \\
+\Iattr{line}{pb}  & Second point of the segment\\
+\Iattr{line}{type} & Type is 'line'\\  
+\Iattr{line}{mid} & Middle of the segment |z.M = L.AB.mid|\\
+\Iattr{line}{slope} & Slope of the line obtained with |an = L.AB.slope|\\
+\Iattr{line}{length} & Length of the segment |l = L.AB.length| \\  
+\Iattr{line}{north\_pa}   & See next example \\
+\Iattr{line}{north\_pb}   & \\
+\Iattr{line}{south\_pa}   & \\
+\Iattr{line}{south\_pb}   & \\
+\Iattr{line}{east}   & \\
+\Iattr{line}{west}   & \\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Example: attributes of class line} % (fold)
+\label{ssub:example_class_line}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+  scale  = .5
+   z.a   = point: new (1, 1)
+   z.b   = point: new (5, 4)
+   L.ab  = line : new (z.a,z.b)
+   z.m   = L.ab.mid
+   z.w   = L.ab.west
+   z.e   = L.ab.east
+   z.r   = L.ab.north_pa
+   z.s   = L.ab.south_pb
+   sl    = L.ab.slope
+   len   = L.ab.length
+   set_lua_to_tex{"sl","len"}
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints(a,b,m,e,r,s,w)
+   \tkzLabelPoints(a,b,e,r,s,w)
+   \tkzLabelPoints[above](m)
+   \tkzDrawLine(a,b)
+   \tkzLabelSegment[sloped](a,b){ab = \len}
+   \tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \sl}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.a = point: new (1, 1)
+z.b = point: new (5, 4)
+L.ab = line : new (z.a,z.b)
+z.m = L.ab.mid
+z.w = L.ab.west
+z.e = L.ab.east
+z.r = L.ab.north_pa
+z.s = L.ab.south_pb
+sl = L.ab.slope
+len = L.ab.length
+set_lua_to_tex{"sl","len"}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(a,b,m,e,r,s,w)
+\tkzLabelPoints(a,b,e,r,s,w)
+\tkzLabelPoints[above](m)
+\tkzDrawLine(a,b)
+\tkzLabelSegment[sloped](a,b){ab = \len}
+\tkzLabelSegment[above=12pt,sloped](a,b){slope of (ab) = \sl}
+\end{tikzpicture}
+\hspace*{\fill}
+% \caption{Class Line}
+% subsubsection example_class_line (end)
+
+\subsubsection{Method \Imeth{line}{new} and line attributes}
+\label{ssub:example_line_attributes}
+
+Notation |L| or |L.AB| or |L.euler|. The notation is actually free.
+|L.AB| can also represent the segment. With | L.AB  = line : new (z.A,z.B)|, a line is defined.
+
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A   = point : new (1,1)
+   z.B   = point : new (3,2)
+   L.AB  = line : new (z.A,z.B)
+   z.C   = L.AB.north_pa
+   z.D   = L.AB.south_pa
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,B C,D)
+   \tkzDrawPoints(A,...,D)
+   \tkzLabelPoints(A,...,D)
+   \tkzMarkRightAngle(B,A,C)
+   \tkzMarkSegments(A,C A,B A,D)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+   scale = 1
+   z.A   = point : new (1,1)
+   z.B   = point : new (3,2)
+   L.AB  = line : new (z.A,z.B)
+   z.C   = L.AB.north_pa
+   z.D   = L.AB.south_pa
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,B C,D)
+   \tkzDrawPoints(A,...,D)
+   \tkzLabelPoints(A,...,D)
+   \tkzMarkRightAngle(B,A,C)
+   \tkzMarkSegments(A,C A,B A,D)
+\end{tikzpicture}
+\end{minipage}
+% subsubsection example_line_attributes (end)
+% subsection attributs_of_a_line (end)
+
+\clearpage\newpage
+\subsection{Methods of the class line} % (fold)
+\label{sub:methods_from_class_line}
+Here's the list of methods for the \tkzNameObj{line} object. The results are either reals, points, lines, circles or triangles.
+\subsubsection{Table of the methods from  class line} % (fold)
+\label{ssub:table_of_the_methods_from_class_line}
+\bgroup
+\catcode`_=12
+\small
+\begin{center}
+%\caption{Methods from  class line}
+\begin{tabular}{ll}
+\toprule
+\textbf{Methods} & \textbf{Comments}  \\
+\midrule 
+\Imeth{line}{new(A, B)}      & |L.AB = line : new(z.A,z.B)| line through the points $A$ and $B$\\
+\midrule 
+ \textbf{Points} &\\
+\midrule 
+\Imeth{line}{gold\_ratio ()}  & |z.C = L.AB : gold_ratio()|   \tkzar gold ratio   \\
+\Imeth{line}{barycenter (ka,kb)}    & |z.C = L.AB : barycenter (1,2)| $C$ --> barycenter of |{(A,1)(B,2)}|\\
+\Imeth{line}{point (t)} & |z.C = L.AB : point (2)| \tkzar  $\overrightarrow{AC} = 2\overrightarrow{AB}$\\
+\Imeth{line}{midpoint ()}    & |z.M = L.AB : midpoint ()| \tkzar better is |z.M = L.AB.mid|  \\
+\Imeth{line}{harmonic\_int }  & |z.D = L.AB : harmonic_int (z.C)| \tkzar $D\in [AB]$ $C\notin [AB]$\\
+\Imeth{line}{harmonic\_ext (pt)}  & |z.D = L.AB : harmonic_ext (z.C)| \tkzar $D\notin [AB]$ $C\in [AB]$\\
+\Imeth{line}{harmonic\_both (k)}  & |z.C,z.D = L.AB : harmonic_both (tkzphi)| \tkzar ${ {CA/CB}={DA/DB}=t\varphi.}$\\
+\Imeth{line}{projection ( pt )}  & |z.H = L.AB : projection (z.C)| \tkzar $CH \perp (AB)$ and $H\in (AB)$\\
+\Imeth{line}{set\_projection (...)}   & projection of a list of points \\
+\Imeth{line}{symmetry\_axial ( pt )}  & |z.Cp = L.AB : symmetry_axial (z.C)|\\
+\Imeth{line}{set\_symmetry\_axial (...) }&symmetry_axial of a list of points  \\
+\Imeth{line}{square ()} & |z.C,z.D = L.AB : square () | \tkzar  creates 2 points to make a square.\\
+\midrule 
+ \textbf{Lines} &\\
+\midrule  
+\Imeth{line}{ll\_from ( pt )}  & |L.CD = L.AB : ll_from  (z.C)| \tkzar $(CD) \parallel (AB)$ \\
+\Imeth{line}{ortho\_from ( pt )} & |L.CD = L.AB : ortho_from  (z.C)| \tkzar $(CD) \perp (AB)$\\
+\Imeth{line}{mediator ()}&|L.uv = L.AB : mediator ()| \tkzar $(u,v)$ mediator of $(A,B)$\\
+\midrule 
+ \textbf{Triangles} &\\
+\midrule  
+\Imeth{line}{equilateral ()}  & |z.C = L.AB : equilateral_tr ()|  $(\overrightarrow{AB},\overrightarrow{AC})>0$    \\
+\Imeth{line}{isosceles (phi)}     & |z.C = L.AB : isosceles (math.pi/6)| \\
+\Imeth{line}{gold ()}     & |z.C = L.AB : gold ()| \tkzar right in $B$ and $AC = \varphi \times AB $ \\
+\Imeth{line}{euclide ()}   & |z.C = L.AB : euclide ()| \tkzar $AB=AC$ and   $(\overrightarrow{AB},\overrightarrow{AC}) = math.pi/5$    \\
+\Imeth{line}{golden ()}    & |z.C = L.AB : golden ()|   $(\overrightarrow{AB},\overrightarrow{AC}) = 2\times math.pi/5$   \\
+\midrule 
+ \textbf{Circles} &\\
+\midrule 
+\Imeth{line}{circle ()}  & |C.AB = L.AB : circle ()| circle center pa through pb \\
+\Imeth{line}{circle\_swap ()}  & |C.BA = L.AB : circle\_swap ()| circle center pb through pa \\
+\midrule 
+ \textbf{Miscellaneous} &\\
+\midrule 
+\Imeth{line}{distance (pt)}   & |d = L.Ab : distance (z.C)|  d=CH with H projection of $C$ onto (AB)\\
+\Imeth{line}{in\_out (pt)}    & |b = L.AB : in_out (z.C)| $b$ is a boolean b=true if $C\in (AB)$ \\
+\Imeth{line}{slope ()} &   |a = L.AB : slope()| \tkzar better is L.AB.slope \\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+% subsubsection table_of_the_methods_from_class_line (end)
+
+Here are a few examples.
+
+\subsubsection{Example: new line from a defined line} % (fold)
+\label{ssub:new_line_from_a_defined_line}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = 1.25
+   z.A   = point : new (1,1)
+   z.B   = point : new (3,2)
+   L.AB  = line : new (z.A,z.B)
+   z.C   = L.AB.north_pa
+   z.D   = L.AB.south_pa
+   L.CD  = line : new (z.C,z.D)
+   _,z.E   = get_points ( L.CD: ll_from (z.B))
+   -- z.E   = L2.pb
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,B C,D B,E)
+   \tkzDrawPoints(A,...,E)
+   \tkzLabelPoints(A,...,E)
+   \tkzMarkRightAngle(B,A,C)
+   \tkzMarkSegments(A,C A,B A,D)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+scale = 1.25
+z.A   = point : new (1,1)
+z.B   = point : new (3,2)
+L.AB  = line : new (z.A,z.B)
+z.C   = L.AB.north_pa
+z.D   = L.AB.south_pa
+L.CD  = line : new (z.C,z.D)
+_,z.E   = get_points ( L.CD: ll_from (z.B))
+-- or  z.E   = L2.pb with |L2 = L.CD: ll_from (z.B)|
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B C,D B,E)
+\tkzDrawPoints(A,...,E)
+\tkzLabelPoints(A,...,E)
+\tkzMarkRightAngle(B,A,C)
+\tkzMarkSegments(A,C A,B A,D)
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+ %  \caption{New line from defined line}
+% subsubsection new_line_from_a_defined_line (end)
+
+
+\subsubsection{Example: projection of several points} % (fold)
+\label{ssub:example_projection_of_several_points}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale     = .8
+   z.a       = point:  new (0, 0)
+   z.b       = point:  new (4, 1)
+   z.c       = point:  new (2, 5)
+   z.d       = point:  new (5, 2)
+   L.ab      = line:   new (z.a,z.b)
+   z.cp,z.dp = L.ab:  set_projection(z.c,z.d)
+\end{tkzelements}
+ \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(a,b c,c' d,d')
+   \tkzDrawPoints(a,...,d,c',d')
+   \tkzLabelPoints(a,...,d,c',d')
+ \end{tikzpicture}
+ \end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+scale  = .8
+z.a    = point:  new (0, 0)
+z.b    = point:  new (4, 1)
+z.c    = point:  new (2, 5)
+z.d    = point:  new (5, 2)
+L.ab        = line:   new (z.a,z.b)
+z.cp,z.dp   = L.ab :  set_projection(z.c,z.d)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(a,b c,c' d,d')
+\tkzDrawPoints(a,...,d,c',d')
+\tkzLabelPoints(a,...,d,c',d')
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+% \caption{Projection of several points}
+% subsubsection example_projection_of_several_points (end)
+
+\subsubsection{Example: combination of methods} % (fold)
+\label{ssub:example_combination_of_methods}
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A     = point: new (0 , 0)
+   z.B     = point: new (6 , 0)
+   z.C     = point: new (1 , 5)
+   T.ABC   = triangle: new (z.A,z.B,z.C)
+   L.AB    = T.ABC.ab
+   z.O     = T.ABC.circumcenter
+   C.OA    = circle: new (z.O,z.A)
+   z.H     = L.AB: projection (z.O)
+   L.ab    = C.OA: tangent_at (z.A)
+   z.a,z.b = L.ab.pa,L.ab.pb
+  -- or z.a,z.b  = get_points (L.ab)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircle(O,A)
+   \tkzDrawSegments[purple](O,A O,B O,H)
+   \tkzDrawArc[red](O,A)(B)
+   \tkzDrawArc[blue](O,B)(A)
+   \tkzDrawLine[add = 2 and 1](A,a)
+   \tkzFillAngles[teal!30,opacity=.4](A,C,B b,A,B A,O,H)
+   \tkzMarkAngles[mark=|](A,C,B b,A,B A,O,H H,O,B)
+   \tkzDrawPoints(A,B,C,H,O)
+   \tkzLabelPoints(A,B,C,H,O)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+scale   = .5
+z.A     = point: new (0 , 0)
+z.B     = point: new (6 , 0)
+z.C     = point: new (1 , 5)
+T.ABC   = triangle: new (z.A,z.B,z.C)
+L.AB    = T.ABC.ab
+z.O     = T.ABC.circumcenter
+C.OA    = circle: new (z.O,z.A)
+z.H     = L.AB : projection (z.O)
+L.ab    = C.OA : tangent_at (z.A)
+z.a,z.b = L.ab.pa,L.ab.pb
+   -- or z.a,z.b  = get_points (L.ab)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircle(O,A)
+\tkzDrawSegments[purple](O,A O,B O,H)
+\tkzDrawArc[red](O,A)(B)
+\tkzDrawArc[blue](O,B)(A)
+\tkzDrawLine[add = 2 and 1](A,a)
+\tkzFillAngles[teal!30,opacity=.4,,size=.5](A,C,B b,A,B A,O,H)
+\tkzMarkAngles[mark=|,size=.5](A,C,B b,A,B A,O,H H,O,B)
+\tkzDrawPoints(A,B,C,H,O)
+\tkzLabelPoints(A,B,C,H,O)
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+% subsubsection example_combination_of_methods (end)
+
+\subsubsection{Example: distance and projection} % (fold)
+\label{ssub:example_distance_and_projection}
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A    = point : new (0 , 0)
+   z.B    = point : new (5 , -2)
+   z.C    = point : new (3 , 3)
+   L.AB   = line : new (z.A,z.B)
+   d      = L.AB : distance (z.C)
+   z.H    = L.AB : projection (z.C)
+   set_lua_to_tex{'d'}
+\end{tkzelements}
+\begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawLines(A,B C,H)
+  \tkzDrawPoints(A,B,C,H)
+  \tkzLabelPoints(A,B,C,H)
+  \tkzLabelSegment[above left,
+                   draw](C,H){$CH = \d$}
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+   z.A    = point : new (0 , 0)
+   z.B    = point : new (5 , -2)
+   z.C    = point : new (3 , 3)
+   L.AB   = line : new (z.A,z.B)
+   d      = L.AB : distance (z.C)
+   z.H    = L.AB : projection (z.C)
+   set_lua_to_tex{'d'}
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B C,H)
+\tkzDrawPoints(A,B,C,H)
+\tkzLabelPoints(A,B,C,H)
+\tkzLabelSegment[above left,draw](C,H){$CH = \d$}
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+% \caption{Method distance with line object}
+% subsubsection example_distance_and_projection (end)
+% subsection methods_from_class_line (end)
+
+% section class_line (end)
+\endinput
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-misc.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-misc.tex
new file mode 100644
index 00000000000..9bb092ce562
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-misc.tex
@@ -0,0 +1,361 @@
+\clearpage\newpage
+ \section{Math constants and functions} % (fold)
+ \label{sec:math_functions}
+
+\bgroup
+\catcode`_=12 
+\small
+\begin{center}
+%\caption{functions\_maths.lua   }
+\begin{tabular}{ll}
+\toprule
+\textbf{contants or functions} & \textbf{Comments}\\
+\midrule
+\Igfct{math}{tkzphi}     &  constant $\varphi  = (1+math.sqrt(5))/2 $\\
+\Igfct{math}{tkzinvphi}   &  constant $1/\varphi  = 1/tkzphi$\\
+\Igfct{math}{tkzsqrtphi}    &  constant $\sqrt{\varphi}= math.sqrt(tkzphi)$    \\
+%round(num, idp)    &  \\
+%tkzround( num, idp )   &   \\
+% Cramer33(a1,a2,a3,b1,b2,b3,c1,c2,c3) &  \\
+% Cramer22(a1,a2,b1,b2)  &   \\
+\Igfct{math}{islinear (z1,z2,z3) }   & Are the points aligned? (z2-z1) $\parallel$ (z3-z1) ?  \\
+\Igfct{math}{isortho (z1,z2,z3)} &  (z2-z1) $\perp$ (z3-z1)  ? boolean\\
+\Igfct{package}{set\_lua\_to\_tex (list)}   & set\_lua\_to\_tex('a','n') defines |\a| and |\n|   \\
+%parabola (a,b,c)   & to get   \\
+\Igfct{math}{value (v) }     &  apply |scale| to the value     \\
+\Igfct{math}{angle\_normalize (a) }   &  to get a value between 0 and $2\pi$ \\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Harmonic division with tkzphi } % (fold)
+\label{ssub:harmonic_division_with_tkzphi}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale =.5
+   z.a = point: new(0,0)
+   z.b = point: new(8,0)
+   L.ab = line: new (z.a,z.b)
+   z.m,z.n = L.ab: harmonic_both (tkzphi)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLine[add= .2 and .2](a,n) 
+   \tkzDrawPoints(a,b,n,m)
+   \tkzLabelPoints(a,b,n,m)
+\end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+   scale =.5
+   z.a = point: new(0,0)
+   z.b = point: new(8,0)
+   L.ab = line: new (z.a,z.b)
+   z.m,z.n = L.ab: harmonic_both (tkzphi)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLine[add= .2 and .2](a,n) 
+   \tkzDrawPoints(a,b,n,m)
+   \tkzLabelPoints(a,b,n,m)
+\end{tikzpicture}
+ \hspace*{\fill}
+% subsubsection harmonic_division_with_tkzphi (end)
+
+\subsubsection{Function islinear} % (fold)
+\label{ssub:function_islinear}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a = point: new (1, 1)
+   z.b = point: new (2, 2)
+   z.c = point: new (4, 4)
+   if islinear (z.a,z.b,z.c) then
+       z.d = point: new (0, 0)
+    else 
+        z.d = point: new (-1, -1)
+   end
+\end{tkzelements}
+\begin{tikzpicture}
+    \tkzGetNodes
+    \tkzDrawPoints(a,...,d)
+    \tkzLabelPoints(a,...,d)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+   z.a = point: new (1, 1)
+   z.b = point: new (2, 2)
+   z.c = point: new (4, 4)
+   if islinear (z.a,z.b,z.c) then
+       z.d = point: new (0, 0)
+    else 
+        z.d = point: new (-1, -1)
+   end
+\end{tkzelements}
+ \hspace*{\fill}
+\begin{tikzpicture}
+    \tkzGetNodes
+    \tkzDrawPoints(a,...,d)
+    \tkzLabelPoints(a,...,d)
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+% subsubsection function_islinear (end)
+
+
+
+
+\subsubsection{Function  \tkzfname{value} }% (fold)
+\label{ssub:function_value}
+
+value to apply scaling if necessary
+
+If |scale = 1.2| with a = value(5) the actual value of |a| will be $5\times 1.2 = 6$.
+
+
+% subsubsection function_value (end)
+
+\subsubsection{Transfer from lua to \TEX} % (fold)
+\label{ssub:transfer_from_lua_to_tex}
+
+ \Igfct{package}{set\_lua\_to\_tex (list)}
+
+see examples \ref{ssub:get_angle}, \ref{ssub:dot_or_scalar_product}
+% subsubsection transfer_from_lua_to_tex (end)
+
+\subsubsection{Normalized angles : Slope of lines (ab), (ac) and (ad)} % (fold)
+\label{sub:normalized_angles}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a      = point: new(0, 0)
+   z.b      = point: new(-3, -3)
+   z.c      = point: new(0, 3)
+   z.d      = point: new(2, -2)
+   angle    = point.arg (z.b-z.a)
+   tex.print('slope of (ab) : '..tostring(angle)..'\\\\')
+   tex.print('slope normalized of (ab) : '..tostring(angle\_normalize(angle))..'\\\\')
+   angle    = point.arg (z.c-z.a)
+   tex.print('slope of (ac) : '..tostring(angle)..'\\\\')
+   tex.print('slope normalized of (ac) : '..tostring(angle\_normalize(angle))..'\\\\')
+   angle    = point.arg (z.d-z.a)
+   tex.print('slope of (ad) : '..tostring(angle)..'\\\\')
+   tex.print('slope normalized of (acd) : '..tostring(angle\_normalize(angle))..'\\\\')
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[red](a,b a,c a,d)
+   \tkzDrawPoints(a,b,c,d)
+   \tkzLabelPoints(a,b,c,d)
+\end{tikzpicture}
+\end{tkzexample}
+\begin{tkzelements}
+  scale = .75
+z.a = point: new(0, 0)
+z.b = point: new(-3, -3)
+z.c = point: new(0, 3)
+z.d = point: new(2, -2)
+angle = point.arg (z.b-z.a)
+tex.print('slope of (ab) : '..tostring(angle)..'\\\\')
+tex.print('slope normalized of (ab) : '..tostring(angle_normalize(angle))..'\\\\')
+angle = point.arg (z.c-z.a)
+tex.print('slope of (ac) : '..tostring(angle)..'\\\\')
+tex.print('slope normalized of (ac) : '..tostring(angle_normalize(angle))..'\\\\')
+angle = point.arg (z.d-z.a)
+tex.print('slope of (ad) : '..tostring(angle)..'\\\\')
+tex.print('slope normalized of (ad) : '..tostring(angle_normalize(angle))..'\\\\')
+\end{tkzelements}
+
+  \hspace*{\fill}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[red](a,b a,c a,d)
+   \tkzDrawPoints(a,b,c,d)
+   \tkzLabelPoints(a,b,c,d)
+\end{tikzpicture}
+ \hspace*{\fill}
+  % \caption{Normalized angles}
+
+
+% subsubsection normalized_angles (end)
+
+\subsubsection{Get angle} % (fold)
+\label{ssub:get_angle}
+
+The function  |get_angle (a,b,c)| gives the angle normalized of $(\overrightarrow{ab},\overrightarrow{ac})$.
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a   = point: new(0, 0)
+   z.b   = point: new(-2, -2)
+   z.c   = point: new(0, 3)
+   angcb = tkzround ( get_angle (z.a,z.c,z.b),3)
+   angbc = tkzround ( get_angle (z.a,z.b,z.c),3)
+   set_lua_to_tex{"angcb","angbc"}
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[red](a,b a,c)
+   \tkzDrawPoints(a,b,c)
+   \tkzLabelPoints(a,b,c)
+   \tkzMarkAngle[->](c,a,b)
+   \tkzLabelAngle(c,a,b){\angcb}
+   \tkzMarkAngle[->](b,a,c)
+   \tkzLabelAngle(b,a,c){\angbc}
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+   scale = 1.2
+   z.a   = point: new(0, 0)
+   z.b   = point: new(-2, -2)
+   z.c   = point: new(0, 3)
+   angcb = tkzround ( get_angle (z.a,z.c,z.b),3)
+   angbc = tkzround ( get_angle (z.a,z.b,z.c),3)
+   set_lua_to_tex{"angcb","angbc"}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines[red](a,b a,c)
+\tkzDrawPoints(a,b,c)
+\tkzLabelPoints(a,b,c)
+\tkzMarkAngle[->](c,a,b)
+\tkzLabelAngle(c,a,b){\angcb}
+\tkzMarkAngle[->](b,a,c)
+\tkzLabelAngle(b,a,c){\angbc}
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+%  \caption{Get angle}
+% subsubsection get_angle (end)
+
+\subsubsection{Dot or scalar product} % (fold)
+\label{ssub:dot_or_scalar_product}
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A    = point: new(0,0)
+   z.B    = point: new(5,0)
+   z.C    = point: new(0,3)
+   T.ABC  = triangle: new (z.A,z.B,z.C)
+   z.A_1,
+   z.B_1,
+   z.C_1  = get_points (T.ABC: anti ())
+   x  = dot_product (z.A,z.B,z.C)
+   set_lua_to_tex{"x"}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawPoints(A,B,C,A_1,B_1,C_1)
+   \tkzLabelPoints(A,B,C,A_1,B_1,C_1)
+   \tkzDrawPolygon[blue](A_1,B_1,C_1)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+ scale  = .6
+ z.A    = point: new(0,0)
+ z.B    = point: new(5,0)
+ z.C    = point: new(0,3)
+ T.ABC  = triangle: new (z.A,z.B,z.C)
+ z.A_1,
+ z.B_1,
+ z.C_1  = get_points (T.ABC: anti ())
+ x  = dot_product (z.A,z.B,z.C)
+ set_lua_to_tex{"x"}
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawPoints(A,B,C,A_1,B_1,C_1)
+   \tkzLabelPoints(A,B,C,A_1,B_1,C_1)
+   \tkzDrawPolygon[blue](A_1,B_1,C_1)
+   \end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+%\caption{Dot or scalar product}
+
+
+The scalar product of the vectors $\overrightarrow{AC}$ and $\overrightarrow{AB}$ is equal to $\x$, so these vectors are orthogonal.
+% subsubsection dot_or_scalar_product (end)
+
+\subsubsection{Alignment or orthogonality} % (fold)
+\label{ssub:alignment_or_orthogonality}
+
+With the functions |islinear| and |isortho|. |islinear(z.a,z.b,z.c)| gives |true| idf the points $a$, $b$ and $c$ are aligned.
+
+|isortho(z.a,z.b,z.c)| gives |true| if the line $(ab)$ is orthogonal to the line $(ac)$.
+% subsection alignment_or_orthogonality (end)
+
+\subsubsection{Other functions} % (fold)
+\label{ssub:other_functions}
+
+Not documented because still in beta version: |parabola|, |Cramer22|, |Cramer33|.
+
+% subsubsection other_functions (end)
+
+% section math_functions (end)
+% % section classes_and_objects (end)
+\endinput
+
+
+
+
+% \bgroup
+% \catcode`_=12
+% \begin{table}[H]
+% \small
+% \begin{center}
+% \caption{functions\_polygons.lua }
+% \begin{tabular}{lll}
+% \toprule
+% \textbf{Functions} & \textbf{Comments}\\
+% \midrule
+% function square (a,b)  \\
+% function parallelogram (a,b,c) \\
+% \bottomrule
+% \end{tabular}
+% \end{center}
+% \end{table}
+% \egroup
+
+
+% \bgroup
+% \catcode`_=12
+% \begin{table}[H]
+% \small
+% \begin{center}
+% \caption{elements\_vectors.lua    }
+% \begin{tabular}{lll}
+% \toprule
+% \textbf{Methods} & \textbf{Comments}\\
+% \midrule
+% vector = {} class vector  \\
+% \Imeth{vector}{function vector:  new (z1,z2)} &  st, ed   \\
+% \Imeth{vector}{function vector: normalize  ()} &\\
+% \bottomrule
+% \end{tabular}
+% \end{center}
+% \end{table}
+% \egroup
+
+
+
+
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-point.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-point.tex
new file mode 100644
index 00000000000..311debb4a6e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-point.tex
@@ -0,0 +1,217 @@
+\newpage
+
+\section{Class point} % (fold)
+\label{sec:class_point}
+
+The first one is the base of the package, it is the class \tkzname{point}. This class is hybrid in the sense that it is as much about points of a plane as complex numbers. The principle is the following: the plane is provided with an orthonormal basis which allows us to determine the placement of a point using its abscissa and ordinate coordinates; in the same way any complex number can simply be considered as a pair of real numbers (its real part and its imaginary part). We can then designate the plane as the complex plane, and the complex number $x+iy$ is represented by the point of the plane with coordinates $(x,y)$. Thus the point $A$ will have affix $z.A$. This affix will be with Lua stored in the table $z$ in the form of a couple of real numbers $(x_A,y_A)$. The first element being the real part of the complex, and the second the imaginary part. There will be an identification between the  and its corresponding affix. More precisely, for Lua the name of the point is the key that allows the table to designate the pair of reals associated to the affix.
+
+Writing |z.A = point: new (2,3) | creates an object of class point where |z.A = 2+3i|. 
+
+
+The creation of a point is done using the following method, but there are other possibilities. If a scaling factor has been given, the method takes it into account.
+
+\subsection{Attributs of a point} % (fold)
+\label{sub:attributs_of_a_point}
+% Method \Imeth{point}{new}
+|z.A = point: new (1,2)|. The point $A$ has coordinates $x=1$ and $y=2$. If you use the notation |z.A| then $A$ will be the reference of a node in \TIKZ\ or in \pkg{tkz-euclide}.
+
+This is the creation of a fixed point with coordinates 1 and 2 and which is named $A$. The notation |z.A| indicates that the coordinates will be stored in a table noted |z| (reference to the notation of the affixes of the complex numbers) that A is the name of the point and the key allowing access to the values. 
+
+\bgroup
+\catcode`_=12
+
+\small
+\begin{center}
+%\caption{Attributes  about point class.}
+\begin{tabular}{ll}
+\toprule
+\textbf{Attributes} & \textbf{Application}\\
+\Iattr{point}{re}  &  |z.a.re|   \tkzar z.a = point:new (2,3) x = z.a.re -> x=2\\
+\Iattr{point}{im}  &  |z.a.im|   \tkzar z.a = point:new (2,3) y= z.a.im -> y=3\\
+\Iattr{point}{type} &  |z.a.type| \tkzar |z.a.type = point|\\  
+\Iattr{point}{argument} &  |z.a.argument| \tkzar |z.a.argument = 0.78539816339745| if z.a = 1+i\\
+\Iattr{point}{module}   &  |z.a.module|   \tkzar |z.a.module = 1.4142135623731| if z.a = 1+i\\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Example:point attributes} % (fold)
+\label{ssub:example_point_attributes}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O   = point: new (0 , 0)
+   z.a   = point: new (2, 3)
+   x     = z.a.re
+   y     = z.a.im
+   ty    = z.a.type
+   arg   = z.a.argument
+   m     = z.a.modulus
+   set_lua_to_tex{"x","y","ty","arg","m"}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzInit[ymax=4,xmax=7]
+   \tkzGrid
+   \tkzDrawPoints(a,O)
+   \tkzLabelPoints[above](O,a)
+   \tkzLabelPoint[below](a){
+   \begin{minipage} {5cm}
+   x=\x\\ y=\y\\ type =\ty\\ argument = \arg \\ module = \m
+    \end{minipage}}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   z.O = point: new (0 , 0)
+   z.a = point: new (2, 3)
+   x = z.a.re
+   y = z.a.im
+   ty = z.a.type
+   arg = z.a.argument
+   m = z.a.modulus
+   set_lua_to_tex{"x","y","ty","arg","m"}
+\end{tkzelements}
+
+ \hspace*{\fill}
+    \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzInit[ymax=5,xmax=7]
+   \tkzGrid
+   \tkzDrawPoints(a,O)
+   \tkzLabelPoints[above](O,a)
+   \tkzLabelPoint[below right](a){
+   \begin{minipage} {5cm}
+   x=\x\\ y=\y\\ type =\ty\\ argument = \arg \\ module = \m
+    \end{minipage}}
+   \end{tikzpicture}
+    \hspace*{\fill}
+ %  \caption{Class Point}
+% subsubsection example_point_attributes (end)
+% subsection attributs_of_a_point (end)
+
+\subsection{Methods of the class point} % (fold)
+\label{sub:methods_of_the_class_point}
+
+The methods described in the following table are standard. You'll find them in most of the examples at the end of this documentation. The result of the different methods presented in the following table is a \tkzNameObj{point}. A word about methods beginning with |set_|. The purpose is to be able to apply a method to a list of points.
+
+\bgroup
+\catcode`_=12
+
+\small
+\begin{center}
+%\caption{Methods from elements\_points.lua    }
+\begin{tabular}{ll}   
+\toprule   
+\textbf{Methods} & \textbf{Application} \\  
+\midrule
+\midrule 
+ \textbf{Points} &\\
+\midrule 
+ new (a,b)    & |z.a = point : new(1,2)| \tkzar  affix z.a=1+2i \\
+ polar (radius, phi)  & |z.a = point : polar(1,math.pi/3)| \tkzar  affix $cos(\pi/3)+sin(\pi/3)i$ \\
+ polar_deg (radius, phi) &    phi in deg    \tkzar  polar coordinates phi deg \\
+ north(d) & see \ref{sub:power_v2}    |d| distance to the point 1 if empty  \\
+ south(d) &   \\
+ east(d)  &   \\
+ west(d)  &   \\
+ symmetry(z) & |z.c = z.a:symmetry(z.b)| \tkzar  c symmetry of b with respect to a\\
+ set\_symmetry (...)  & |z.bp,z.cp = z.a : symmetry(z.b,z.c)| \tkzar  list of points\\
+ rotation(angle , pt)    & |z.c = z.a : rotation (math.pi/2,z.b)| \tkzar affix; rotation center a\\
+ set\_rotation (angle,...)&     \\
+ homothety(k,pt)     & |z.c = z.a : homothety (2,z.b)|     \\
+ set\_homothety (k,...)   &    \\
+ normalize() &  |z.b = z.a: normalize () | \tkzar  |z.b| = 1  and z.a = k$\times$ z.b \\
+\bottomrule % 
+\end{tabular}
+\end{center}
+
+ \egroup
+
+
+\subsubsection{Example: method \Imeth{point}{polar} } % (fold)
+\label{ssub:example_polar_method}
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale   = .5
+   z.O     = point:   new  (0, 0)
+   z.A     = point:   new  (3, 0)
+   z.F     = point:   polar (3, math.pi/6)
+\end{tkzelements}
+   \begin{tikzpicture}
+      \tkzGetNodes 
+      \tkzDrawCircle(O,A)
+      \tkzDrawSegments[new](O,A)
+      \tkzDrawSegments[purple](O,F)
+      \tkzDrawPoints(A,O,F)
+      \tkzLabelPoints(A,O,F)
+   \end{tikzpicture}
+   \end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+    scale   = .5
+    z.O     = point:   new  (0, 0)
+    z.A     = point:   new  (3, 0)
+    z.F     = point:   polar (3, math.pi/6)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes 
+\tkzDrawCircle(O,A)
+\tkzDrawSegments[new](O,A)
+\tkzDrawSegments[purple](O,F)
+\tkzDrawPoints(A,O,F)
+\tkzLabelPoints(A,O,F)
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+%   \caption{Method polar}
+
+% subsubsection example_polar_method (end)
+
+\subsubsection{Example: rotation of points method \Imeth{point}{set\_rotation}} % (fold)
+\label{ssub:example_rotation_of_points}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+    z.a        = point:  new(0, -1)
+    z.b        = point:  new(4, 0)
+    z.o        = point:  new(6, -2)
+    z.ap,z.bp  =  z.o : set_rotation (math.pi/2,z.a,z.b)
+\end{tkzelements}
+\begin{tikzpicture}
+    \tkzGetNodes
+    \tkzDrawLines(o,a o,a' o,b o,b')
+    \tkzDrawPoints(a,a',b,b',o)
+    \tkzLabelPoints(a,a',b,b',o)
+    \tkzDrawArc(o,a)(a')
+    \tkzDrawArc(o,b)(b')
+ \end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+    scale = .5
+ z.a = point:  new(0, -1)
+ z.b = point:  new(4, 0)
+ z.o = point:  new(6, -2)
+ z.ap,z.bp =  z.o : set_rotation (math.pi/2,z.a,z.b)
+\end{tkzelements}
+    
+
+\hspace*{\fill}
+    \begin{tikzpicture}
+    \tkzGetNodes
+    \tkzDrawLines(o,a o,a' o,b o,b')
+    \tkzDrawPoints(a,a',b,b',o)
+    \tkzLabelPoints(a,a',b,b',o)
+    \tkzDrawArc(o,a)(a')
+    \tkzDrawArc(o,b)(b')
+    \end{tikzpicture}
+\hspace*{\fill}
+%\caption{Rotation of points}
+% subsubsection example_rotation_of_points (end)
+% subsection methods_of_the_class_point (end)
+% section class_point (end)
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-triangle.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-triangle.tex
new file mode 100644
index 00000000000..2b3056ff924
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-triangle.tex
@@ -0,0 +1,220 @@
+\newpage
+\section{Classe triangle} % (fold)
+\label{sec:classe_triangle}
+
+\subsection{Attributs of a triangle} % (fold)
+\label{sub:attributs_of_a_triangle}
+The triangle object is created using the \Imeth{triangle}{new} method, for example with | T.abc = triangle : new (z.a,z.b,z.c)| (See examples:  \ref{sub:alternate}; \ref{sub:apollonius_circle}; \ref{sub:excircle} ). Multiple attributes are then created.
+
+\bgroup
+\catcode`_=12
+\small
+\begin{center}
+%\caption{Attributes about triangle class.}
+\begin{tabular}{ll}
+\toprule
+\textbf{Attributes}     & \textbf{Application}\\
+\Iattr{triangle}{pa} &\\
+\Iattr{triangle}{pb} &\\
+\Iattr{triangle}{pc} &\\
+\Iattr{triangle}{circumcenter} & \\
+\Iattr{triangle}{centroid} &\\
+\Iattr{triangle}{incenter} &\\
+\Iattr{triangle}{orthocenter}  &\\
+\Iattr{triangle}{eulercenter} &  \\
+\Iattr{triangle}{a}& It's the length of the side opposite the first vertex  \\
+\Iattr{triangle}{b}& It's the length of the side opposite the second verte\\
+\Iattr{triangle}{c}& It's the length of the side opposite the third vertex \\
+\Iattr{triangle}{alpha}& Vertex angle of the first vertex\\
+\Iattr{triangle}{beta}& Vertex angle of the second vertex\\
+\Iattr{triangle}{gamma}&    Vertex angle of the third vertex\\
+\Iattr{triangle}{ab}&    Line defined by the first two points of the triangle\\
+\Iattr{triangle}{ac}& Line defined by the first point and the last point\\
+\Iattr{triangle}{bc}&  Line defined by the last two points of the triangle\\
+\bottomrule %
+\end{tabular}
+\end{center}
+\egroup
+
+\subsubsection{Example: triangle attributes} % (fold)
+\label{ssub:example_triangle_attributes}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a   = point: new (0 , 0)
+   z.b   = point: new (4 , 0)
+   z.c   = point: new (0 , 3)
+   T.abc = triangle : new (z.a,z.b,z.c)
+   z.O   = T.abc.circumcenter
+   z.I   = T.abc.incenter
+   z.H   = T.abc.orthocenter
+   z.G   = T.abc.centroid
+   a     = T.abc.a
+   b     = T.abc.b
+   c     = T.abc.c
+   alpha =  T.abc.alpha
+   beta  =  T.abc.beta
+   gamma =  T.abc.gamma
+   set_lua_to_tex{"a","b","c","alpha","beta","gamma"}
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(a,b,c)
+   \tkzDrawPoints(a,b,c,O,G,I,H)
+   \tkzLabelPoints(a,b,c,O,G,I)
+   \tkzLabelPoints[above right](H)
+   \tkzDrawCircles(O,a)
+   \tkzLabelSegment[sloped](a,b){\c}
+   \tkzLabelSegment[sloped,above](b,c){\a}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale = 1.2
+   z.a = point: new (0 , 0)
+   z.b = point: new (4 , 0)
+   z.c = point: new (0 , 3)
+   T.abc = triangle : new (z.a,z.b,z.c)
+   z.O = T.abc.circumcenter
+   z.I = T.abc.incenter
+   z.H = T.abc.orthocenter
+   z.G = T.abc.centroid
+   a = T.abc.a
+   b = T.abc.b
+   c = T.abc.c
+   alpha =  T.abc.alpha
+   beta =  T.abc.beta
+   gamma =  T.abc.gamma
+   set_lua_to_tex{"a","b","c","alpha","beta","gamma"}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(a,b,c)
+\tkzDrawPoints(a,b,c,O,G,I,H)
+\tkzLabelPoints(a,b,c,O,G,I)
+\tkzLabelPoints[above right](H)
+\tkzDrawCircles(O,a)
+\tkzLabelSegment[sloped](a,b){\c}
+\tkzLabelSegment[sloped,above](b,c){\a}
+\end{tikzpicture}
+\hspace*{\fill}
+%  \caption{Class Triangle}
+% subsubsection example_triangle_attributes (end)
+
+% subsection attributs_of_a_triangle (end)
+
+\subsection{Methods of the class triangle} % (fold)
+\label{sub:methods_of_the_class_triangle}
+
+\bgroup
+\catcode`_=12
+\small
+\begin{minipage}{\textwidth}
+\begin{center}
+%\caption{Methods of the class triangle}
+\begin{tabular}{ll}
+\toprule
+\textbf{Methods} & \textbf{Comments}     \\
+\midrule
+triangle = {} class triangle   \\
+\Imeth{triangle}{new} (a, b ,c) & |T.ABC = triangle : new (z.A,z.B,z.C)|    \\
+ ... & |T| or |T.name| with what you want for name, is possible.\\
+\midrule 
+ \textbf{Points} &\\
+\midrule 
+\Imeth{triangle}{lemoine\_point ()} &  |T.ABC : lemoine_point ()| intersection os the symmedians\\
+\Imeth{triangle}{symmedian\_point ()}  & Lemoine point  or the Grebe point \\
+\Imeth{triangle}{bevan\_point ()}  &  Circumcenter of the excentral triangle\\
+\Imeth{triangle}{mittenpunkt\_point ()}  &  Symmedian point of the excentral triangle\\
+\Imeth{triangle}{gergonne\_point ()}  & Intersection of the three cevians that lead to the contact points \\
+\Imeth{triangle}{nagel\_point () } & Intersection of the three cevians that lead to the extouch points\\
+\Imeth{triangle}{feuerbach\_point () } & The point at which the incircle and euler circle are tangent. \\
+\Imeth{triangle}{spieker\_center ()} &  Incenter of the medial triangle \\
+\Imeth{triangle}{barycenter (ka,kb,kc)} & |T.ABC: barycenter (2,1,1)| barycenter of |({A,2},{B,1},{C,1}) |\\
+\Imeth{triangle}{base (u,v)  }  &  |z.D = T.ABC: base(1,1)| \tkzar ABDC is a parallelogram   \\
+\Imeth{triangle}{projection (p) }   &  Projection of a point on the sides \\
+\Imeth{triangle}{euler\_points () } & Euler points of euler circle   \\
+\Imeth{triangle}{nine\_points () }   &  Points of the euler circle  \\
+\Imeth{triangle}{parallelogram ()} & |z.D = T.ABC : parallelogram ()| \tkzar ABCD is a parallelogram\\
+\midrule
+ \textbf{Lines} &\\
+\midrule 
+\Imeth{triangle}{altitude (n) }  & |L.AHa = T.ABC : altitude () | n empty or 0  line from $A$  
+\footnote{|z.Ha = L.AHa.pb| recovers the common point of the opposite side and altitude. The method |orthic| is usefull.}\\
+\Imeth{triangle}{bisector (n) }  & |L.Bb = T.ABC : bisector (1) |  n = 1   line from $B$     \footnote{|_,z.b = get_points(L.Bb)| recovers the common point of the opposite side and bisector. }\\
+\Imeth{triangle}{bisector\_ext(n) }   &   n=2  line from the third vertex.\\
+\Imeth{triangle}{symmedian\_line (n)}  & Cevian with respect to Lemoine point. \\
+\Imeth{triangle}{euler\_line () } & the line through $N$ ,$G$, $H$ and $O$ if the triangle is not equilateral
+\footnote{N center of nine points circle, G centroid, H orthocenter , O circum center } \\
+\Imeth{triangle}{antiparallel(pt,n)} & n=0 antiparallel through pt to $(BC)$, n=1 to $(AC)$ etc.\\
+\bottomrule
+\end{tabular}
+\end{center}
+\end{minipage}
+\egroup
+
+\clearpage\newpage
+\bgroup
+\catcode`_=12
+\small
+\begin{minipage}{\textwidth}
+\begin{center}
+%\caption{Methods of the class triangle (follow-up) }
+\begin{tabular}{ll}
+\toprule
+\textbf{Methods} & \textbf{Comments}     \\
+\midrule 
+ \textbf{Circles} &\\
+\midrule 
+\Imeth{triangle}{euler\_circle ()} & C.|NP = T.ABC : euler_circle ()| \tkzar $N$ euler point 
+ \footnote{ The midpoint of each side of the triangle, the foot of each altitude, the midpoint of the line segment from each vertex of the triangle to the orthocenter.}   \\
+\Imeth{triangle}{circum\_circle ()}  & |C.OA = T.ABC : circum ()| Triangle's circumscribed circle \\
+\Imeth{triangle}{in\_circle ()}  &   Inscribed circle of  the triangle\\
+\Imeth{triangle}{ex\_circle (n)}  &  Circle tangent to three lines defined by the sides of the triangle \\
+\Imeth{triangle}{first\_lemoine\_circle ()}  & The center is the midpoint between Lemoine point and the circumcenter.\footnote{
+Through the Lemoine point draw lines parallel to the triangle's sides. The points where the parallel lines intersect the sides of ABC
+ then lie on a circle known as the first Lemoine circle. } \\
+\Imeth{triangle}{second\_lemoine\_circle ()} & see example \ref{sub:antiparallel_through_lemoine_point}\\
+\Imeth{triangle}{spieker\_circle ()} & The incircle of the medial triangle\\
+\Imeth{triangle}{ex\_circle(n) }  & |z.o,z.p,z.q,z.r  = T.ABC: ex_circle ()|\\
+... & n=0 ex_circle opposed to $A$ p,q,r projections of o  on the sides  \\
+\midrule 
+ \textbf{Triangles} &\\
+\midrule 
+\Imeth{triangle}{orthic ()}  &  |T = T.ABC : orthic ()| triangle joining the feet of the altitudes   \\
+\Imeth{triangle}{medial ()}  &   |T = T.ABC : medial ()| triangle with vertices at the midpoints\\
+\Imeth{triangle}{incentral ()}    &   Cevian triangle of the triangle with respect to its incenter \\
+\Imeth{triangle}{excentral ()  }  &   Triangle with vertices corresponding to the excenters   \\
+\Imeth{triangle}{extouch ()}  & Triangle formed by the points of tangency with the excircles    \\
+\Imeth{triangle}{intouch () } &  Contact triangle formed by the points of tangency of the incircle \\
+\Imeth{triangle}{tangential ()} & Triangle formed by the lines tangent to the circumcircle at the vertices\\
+\Imeth{triangle}{feuerbach ()} & Triangle formed by the points of tangency of the euler circle with the excircles\\
+\Imeth{triangle}{anti () }&  Anticomplementary Triangle The given triangle is its medial triangle.   \\
+\Imeth{triangle}{cevian (pt)} & Triangle formed with the endpoints of the three cevians with respect to |pt|.\\
+\Imeth{triangle}{symmedian ()} & Triangle formed with the intersection points of the symmedians. \\
+\Imeth{triangle}{euler ()} &  Triangle formed with the euler points \\
+\midrule 
+\midrule 
+ \textbf{Miscellaneous} &\\
+\midrule 
+\Imeth{triangle}{area ()}   & $ \mathcal{A}$| = T.ABC: area ()|\\
+\Imeth{triangle}{barycentric\_coordinates (pt)} & Triples of numbers corresponding to masses placed at the vertices\\
+\Imeth{triangle}{in\_out (pt)}  & Boolean. Test if |pt| is inside the triangle\\
+\Imeth{triangle}{check\_equilateral ()} & Boolean. Test if the triangle is equilateral\\
+\bottomrule
+\end{tabular}
+\end{center}
+\end{minipage}
+\egroup
+% subsubsection methods_of_the_class_triangle (end)
+
+
+
+% subsection methods_of_the_class_triangle (end)
+
+
+
+% section classe_triangle (end)
+\endinput
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes.tex
new file mode 100644
index 00000000000..53bdb06558c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes.tex
@@ -0,0 +1,98 @@
+\newpage
+\section{Classes and objects} % (fold)
+\label{sec:classes_and_objects}
+
+\subsection{Objects} % (fold)
+\label{sub:objects}
+The object types currently defined and used are \tkzNameObj{point}, \tkzNameObj{line}, \tkzNameObj{circle}, \tkzNameObj{triangle} and \tkzNameObj{ellipse}. 
+
+They can be created directly using the method \Imeth{obj}{new} and, with the exception of the \Iclass{class}{point} class, by giving points. Objects can also be obtained by applying methods to other objects. For example, |T.ABC : circum_circle ()| creates an object \tkzNameObj{circle}. Some object attributes are also objects, such as |T.ABC.bc| which creates the object \tkzNameObj{line}, a straight line passing through the last two points defining the triangle.
+
+Attributes are accessed using the classic method, so |T.pc| gives the third of the triangle and |C.center| gives the center of the circle, but I've added a |get_points| function that returns the points of an object. This applies to straight lines (pa and pc), triangles (pa, pb and pc) and circles (center and through).
+
+Example: |z.O,z.T = get_points (C)| recovers the center and a point of the circle.
+% subsection objects (end)
+
+\subsection{tkz\_elements\_point.lua: complex numbers library} % (fold)
+\label{sub:complex_numbers}
+
+Unless you want to create your own functions, you won't need to know and use complex numbers. However, in some cases it may be useful to implement some of their properties.
+
+|za =  point (1,2 )| and \ |zb = point (1,-1)| define two affixes which are |za = 1+2i| and 
+
+ |zb = 1-i|. The notation may come as a surprise, as I used the term "point". The aim here was not to create a complete library on complex numbers, but to be able to use their main properties in relation to points. I didn't want to have two different levels, and since a unique connection can be established between the points of the plane and the complexes, I decided not to mention the complex numbers! But they are there.
+
+The above entries must not be confused with the following ones : 
+
+|z.a = point : new (1,2) | and |z.b = point : new (1,-1) |. 
+
+Here we define two "point" objects that are in the form of an affix in the |z| table.
+|z.a = za| only if |scale = 1|  and |z.a| creates a point named |a|. This point is an object and you can use its attributes, as well as methods referring to points.
+
+That said, |z.a| is indeed an affix, and it's possible to use the methods and metamethods associated with complex numbers. 
+
+\bgroup
+\catcode`_=12  
+\small
+\begin{minipage}{\textwidth}
+\begin{center}
+%\caption{Metamethods and methods about point class.}
+\begin{tabular}{ll}   
+  \toprule   
+  \textbf{Metamethods} & \textbf{Application} \\     
+  \midrule      
+__add(z1,z2)   & |z.a + z.b| \tkzar affix \\
+__sub(z1,z2)   & |z.a - z.b| \tkzar affix\\
+__unm(z)   & |- z.a| \tkzar affix\\
+__mul(z1,z2)   & |z.a * z.b|  \tkzar  affix\\
+__concat(z1,z2)& |z.a .. z.b| \tkzar dot product  = real number \footnote{If $O$ is the origin of the complex plan, then we get the dot product of the vectors $\overrightarrow{Oa}$ and $\overrightarrow{Ob}$} \\
+__pow(z1,z2)   & |z.a ^ z.b| \tkzar determinant = real number\\
+__div(z1,z2)   & |z.a / z.b|   \tkzar   affix     \\
+__tostring(z)  & tex.print(tostring(z)) \tkzar displays the affix   \\
+__tonumber(z)  & tonumber(z) \tkzar affix or nil\\
+__eq(z1,z2)    &  eq (z.a,z.b) \tkzar boolean\\
+\bottomrule
+\end{tabular}
+\end{center}
+\end{minipage}
+\egroup
+
+\bgroup
+\catcode`_=12  
+\small
+\begin{center}
+%\caption{Metamethods and methods about point class.}
+\begin{tabular}{ll}   
+  \toprule    
+\textbf{Methods} & \textbf{Application}\\     
+\midrule     
+\Imeth{point}{conj(z)}& |z.a : conj()|  \tkzar affix (conjugate) \\
+\Imeth{point}{mod(z)}& |z.a : mod()|   \tkzar real number = modulus  |z.a|\\
+\Imeth{point}{abs (z)}& |z.a : abs()|   \tkzar real number = modulus \\
+\Imeth{point}{norm (z)} & |z.a : norm()|  \tkzar norm  (real number  ) \\
+\Imeth{point}{arg (z)}& |z.a : arg()|   \tkzar real number = argument of z.a (in rad)\\
+\Imeth{point}{get(z)}& |z.a : get()|   \tkzar re and im (two real numbers  )  \\
+\Imeth{point}{sqrt(z)}& |z.a : sqrt()|  \tkzar affix  \\
+\bottomrule
+\end{tabular}
+\end{center}
+\egroup
+
+The class is provided with two specific metamethods.
+
+\begin{itemize}
+   \item Since concatenation makes little sense here, the operation associated with |..| is the scalar or dot product. If |z1 = a+ib| and |z2 = c+id| then 
+   
+   |z1..z2 = (a+ib) .. (c+id) = (a+ib) (c-id) = ac+bd + i(bc-ad) |  
+   
+   There's also a mathematical function, |dot_product|, which takes three arguments. See example \ref{ssub:dot_or_scalar_product}
+
+   
+   \item With the same idea, the operation associated with |^| is the determinant i.e.
+   
+   |z1 ^ z2 = (a+ib) ^ (c+id) = ad - bc  From  (a-ib) (c+id) = ac+bd + i(ad - bc)| we take the imaginary part.
+   
+\end{itemize}
+% subsection complex_numbers (end)
+% section classes_and_objects (end)
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-convention.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-convention.tex
new file mode 100644
index 00000000000..916e6bd1fb3
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-convention.tex
@@ -0,0 +1,88 @@
+\newpage
+
+\section{Writing Convention} % (fold)
+\label{sec:writing_convention}
+
+Writing conventions for real numbers are the same as for \pkg{Lua}.
+The package introduces complex numbers (see \ref{sub:complex_numbers}) in order to associate them with points. |z1 = point (1,2)| designates the affix |z1=1+2i|, |z1| is a complex number, but here it's not a object point (related to objects in object-oriented programming). 
+
+|z.A = point : new (1,2)| creates an object point $A$ with coordinates 1 and 2, which are stored as an affix in the table |z|. The key is $A$ and the value |1+2i| (or (1,2) if you prefer.)
+
+\subsection{Assigning a Name to a Point} % (fold)
+\label{sub:assigning_a_name_to_a_point}
+The basic object is the point which belongs to the class point. A point can be created in two ways: either directly |z.A = point : new (1,2)|, or as the result of a function or a method.
+
+Currently the only obligation is to store the points in the table |z| \footnote{To place the point M in the table, simply write |z.M| = \ldots or |z["M"]|= \ldots} if you want to use them in \TIKZ\ or \pkg{tkz-euclide}. If it is a point which will not be used, then you can designate it as you wish by respecting the conventions of Lua. 
+
+More generally, with |z.A = point: new (a,b)|, we define a complex number |z.A = a+bi|, where $a$ and $b$ are the coordinates of point $A$. The name $A$ of a point is the key associated with a complex number noted |z.A| whose affix is |a+ib|, with $a$ and $b$ unique coordinates of $A$.
+
+
+There are two cases. Either you want to keep the point to use it with the package that will allow you to draw, or the point is intermediate and you can abandon it.
+
+\vspace{12pt}
+In the second case, simply don't store the point in the |z| table. For example, |A = point : new (1,2)| defines a point $A$ that will not be transferred. Another way of avoiding a transfer is to assign |nil| to the point: |z.A = nil| before exiting the environment \tkzNameEnv{elements}.
+
+ In the first case, you must store the point in the table |z|. The points which occur in the  environment \tkzNameEnv{elements} must respect a convention which is |z.name| such that |name| will be the name of the corresponding \tkzname{node}. \footnote{ However, that a point can be deleted with |z.name = nil|.}
+ 
+What are the conventions for designating |name|? You have to respect the Lua conventions in  particular cases.
+\begin{enumerate}
+
+   \item  The use of prime is problematic. If the point name contains more than one symbol and ends with |p|  then when passing into \pkg{TikZ} or \pkg{tkz-euclide}, the letters |p|  will be replaced by |'| using the macro \tkzcname{tkzGetNodes}; \index{prime}
+ 
+   \item  One possibility, however, in order to have a more explicit code is to suppose that you want to designate a point by "euler". It would be possible for example to write |euler = ...|, and at the end of the code for the transfer, |z.E = euler|. It is also possible to use a temporary name |euler| and to replace it in \TIKZ{}. Either at the time of placing the labels, or for example by using |pgfnodealias{E}{euler}|. This possibility also applies in other cases: prime, double prime, etc.
+   
+\end{enumerate}
+
+\lefthand\ The syntax  |z.name| is important, it allows to store the data of the point in a table named |z|, which will be used for the transition to the program that will perform the plots and place the labels.
+
+Point names: You can use the lower case and unaccented upper case.
+
+The names of the points follow the rules of convention for writing identifiers in lua.
+The name starts with a letter "A to Z" or "a to z" or an underscore "|_|" followed by zero or more letters, underscores, and digits (0 to 9).
+
+You should avoid identifiers starting with an underscore followed by one or more uppercase letters.
+
+In general, the points used in geometry are lower or upper case letters. The use of underscore is also frequent. So it is possible to write |z.T_a|.
+
+\lefthand\ Another use in geometry that can be used with \TIKZ{} is the apostrophe. Unfortunately, the apostrophe is necessary to use strings. There are several ways to get around this difficulty.
+The simplest one, which keeps the syntax consistent, is that if you want to use |A'| as a point name, you can use |Ap|. When switching to \TIKZ{} |Ap| will be replaced by |A'|. All names of more than one character ending in |p| will have the letter |p| replaced by an apostrophe |'|.
+% subsection assigning_a_name_to_a_point (end)
+
+\subsection{Assigning a Name to Other Objects} % (fold)
+\label{sub:assigning_a_name_to_other_objects}
+
+You have the choice to give a name to objects other than points. That said, it is preferable to respect certain rules in order to make the code easier to read.
+I have chosen for my examples the following conventions: first of all I store the objects in tables: |L.name| for lines and segments, |C.name| for circles, |T.name| for triangles, |E.name| for ellipses.
+
+For lines, I use the names of the two points. So if a line passes through points $A$ and $B$, I name the line |L.AB|. It is possible if only one line is named to simply name it |L| but this should be avoided so as not to create bad practices.
+
+For circles, I name |C.AB| the circle of center $A$ passing through $B$, but siomething like |C.euler| or |C.external| is fine.
+
+For triangles, I name |T.ABC| the triangle whose vertices are $A$, $B$ and $C$.
+
+For ellipses, I name |E.ABC| the ellipse with center $A$ through vertex $B$ and covertex $C$.
+% subsection assigning_a_name_to_other_objects(end)
+
+\subsection{Writing conventions for attributes, methods.} % (fold)
+\label{sub:writing_conventions_for_attributs_methods_and_functions}
+
+You must use the conventions of Lua, so
+
+\begin{itemize}
+   \item To obtain an attribute, for all objects, the convention is identical: |object.attribute|. For example, for the point $A$ we access its abscissa with |z.A.re| and its ordinate with |z.A.im|; as for its type we obtain it with |z.A.type|. To get the south pole of the circle |C.OA| you need to write: |C.OA.south|.
+   
+   \item To use a method such as obtaining the incircle of a triangle ABC, just write 
+   
+   |z.i,z.i_a,z.i_b,z.i_c = T.ABC : in_circle ()| (you get the center and its projections on the sides), but to get only the incenter you write |T.ABC.incenter|. 
+   
+   \item Some methods need a parameter. For example, to know the distance between a point  $C$  to the line $(A,B)$ we will write 
+   
+   |d = L.AB : distance (z.C)|.
+   
+   \item Use the underscore to store a result you don't want to use. If you only need the second point of an intersection between a line and a circle, you would write 
+   
+   |_,z.J = intersection (L.AB , C.OC)|.
+
+\end{itemize}
+% section writing_convention (end)
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-examples.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-examples.tex
new file mode 100644
index 00000000000..bcf0ccacce0
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-examples.tex
@@ -0,0 +1,4308 @@
+\newpage
+
+\section{Examples} % (fold)
+\label{sec:examples}
+   
+\subsection{D'Alembert 1} % (fold)
+\label{sub:d_alembert_1}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A = point : new (0,0)
+   z.a = point : new (4,0)
+   z.B = point : new (7,-1)
+   z.b = point : new (5.5,-1)
+   z.C = point : new (5,-4)
+   z.c = point : new (4.25,-4)
+   C.Aa    = circle :    new (z.A,z.a)
+   C.Bb    = circle :    new (z.B,z.b)
+   C.Cc    = circle :    new (z.C,z.c)
+   z.I = C.Aa : external_similitude (C.Bb)
+   z.J = C.Aa : external_similitude (C.Cc)
+   z.K = C.Cc : external_similitude (C.Bb)
+   z.Ip    = C.Aa : internal_similitude (C.Bb)
+   z.Jp    = C.Aa : internal_similitude (C.Cc)
+   z.Kp    = C.Cc : internal_similitude (C.Bb)
+\end{tkzelements}
+\begin{tikzpicture}[rotate=-60]
+   \tkzGetNodes
+   \tkzDrawCircles(A,a B,b C,c)
+   \tkzDrawPoints(A,B,C,I,J,K,I',J',K')
+   \tkzDrawSegments[new](I,K A,I A,J B,I B,K C,J C,K)
+   \tkzDrawSegments[purple](I,J' I',J I',K)
+   \tkzLabelPoints(I,J,K,I',J',K')
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.A = point : new (0,0)
+z.a = point : new (4,0)
+z.B = point : new (7,-1)
+z.b = point : new (5.5,-1)
+z.C = point : new (5,-4)
+z.c = point : new (4.25,-4)
+C.Aa    = circle :    new (z.A,z.a)
+C.Bb    = circle :    new (z.B,z.b)
+C.Cc    = circle :    new (z.C,z.c)
+z.I = C.Aa : external_similitude (C.Bb)
+z.J = C.Aa : external_similitude (C.Cc)
+z.K = C.Cc : external_similitude (C.Bb)
+z.Ip    = C.Aa : internal_similitude (C.Bb)
+z.Jp    = C.Aa : internal_similitude (C.Cc)
+z.Kp    = C.Cc : internal_similitude (C.Bb)
+\end{tkzelements}
+
+\hspace*{\fill}  
+\begin{tikzpicture}[rotate=30]
+   \tkzGetNodes
+   \tkzDrawCircles(A,a B,b C,c)
+   \tkzDrawPoints(A,B,C,I,J,K,I',J',K')
+   \tkzDrawSegments[new](I,K A,I A,J B,I B,K C,J C,K)
+   \tkzDrawSegments[purple](I,J' I',J I',K)
+   \tkzLabelPoints(I,J,K,I',J',K')
+\end{tikzpicture}
+\hspace*{\fill}
+\vspace*{\fill}
+%\caption{D'Alembert I}
+
+% subsection d_alembert_1 (end)
+
+\subsection{D'Alembert 2} % (fold)
+\label{sub:d_alembert_2}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = .75
+   z.A     = point : new (0,0)
+   z.a     = point : new (5,0)
+   z.B     = point : new (7,-1)
+   z.b     = point : new (3,-1)
+   z.C     = point : new (5,-4)
+   z.c     = point : new (2,-4)
+   C.Aa    = circle :    new (z.A,z.a)
+   C.Bb    = circle :    new (z.B,z.b)
+   C.Cc    = circle :    new (z.C,z.c)
+   z.i,z.j = get_points (C.Aa : radical_axis (C.Bb))
+   z.k,z.l = get_points (C.Aa : radical_axis (C.Cc))
+   z.m,z.n = get_points (C.Bb : radical_axis (C.Cc))
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(A,a B,b C,c)
+   \tkzDrawLines[new](i,j k,l m,n)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale = .75
+   z.A     = point : new (0,0)
+   z.a     = point : new (5,0)
+   z.B     = point : new (7,-1)
+   z.b     = point : new (3,-1)
+   z.C     = point : new (5,-4)
+   z.c     = point : new (2,-4)
+   C.Aa    = circle :    new (z.A,z.a)
+   C.Bb    = circle :    new (z.B,z.b)
+   C.Cc    = circle :    new (z.C,z.c)
+   z.i,z.j = get_points (C.Aa : radical_axis (C.Bb))
+   z.k,z.l = get_points (C.Aa : radical_axis (C.Cc))
+   z.m,z.n = get_points (C.Bb : radical_axis (C.Cc))
+\end{tkzelements}
+
+\hspace*{\fill} 
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(A,a B,b C,c)
+\tkzDrawLines[new](i,j k,l m,n)
+\end{tikzpicture}
+\hspace*{\fill} 
+%\caption{D'alembert II}
+
+% subsection d_alembert_2 (end)
+
+\subsection{Alternate} % (fold)
+\label{sub:alternate}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (6 , 0)
+   z.C  = point: new (1 , 5)
+   T    = triangle: new (z.A,z.B,z.C)
+   z.I  = T.incenter
+   L.AI = line: new (z.A,z.I) 
+   z.D  = intersection (L.AI,T.bc)
+   L.LLC    = T.ab: ll_from (z.C)
+   z.E  = intersection (L.AI,L.LLC)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawLine[purple](C,E)
+   \tkzDrawSegment[purple](A,E)
+   \tkzFillAngles[purple!30,opacity=.4](B,A,C C,E,D)
+   \tkzMarkAngles[mark=|](B,A,D D,A,C C,E,D)
+   \tkzDrawPoints(A,...,E)
+   \tkzLabelPoints(A,B)
+   \tkzLabelPoints[above](C,D,E)
+   \tkzMarkSegments(A,C C,E)
+\end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+z.A  = point: new (0 , 0)
+z.B  = point: new (6 , 0)
+z.C  = point: new (1 , 5)
+T    = triangle: new (z.A,z.B,z.C)
+z.I  = T.incenter
+L.AI = line: new (z.A,z.I) 
+z.D  = intersection (L.AI,T.bc)
+L.LLC    = T.ab: ll_from (z.C)
+z.E  = intersection (L.AI,L.LLC)
+\end{tkzelements}
+
+\hspace*{\fill} 
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawLine[purple](C,E)
+\tkzDrawSegment[purple](A,E)
+\tkzFillAngles[purple!30,opacity=.4](B,A,C C,E,D)
+\tkzMarkAngles[mark=|](B,A,D D,A,C C,E,D)
+\tkzDrawPoints(A,...,E)
+\tkzLabelPoints(A,B)
+\tkzLabelPoints[above](C,D,E)
+\tkzMarkSegments(A,C C,E)
+\end{tikzpicture}
+\hspace*{\fill}
+
+% subsection alternate (end)
+
+\subsection{Apollonius circle} % (fold)
+\label{sub:apollonius_circle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+scale=.75
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (6 , 0)
+   z.M      = point: new (5 , 3)
+   T.MAB    = triangle : new (z.M,z.A,z.B)
+   L.bis    = T.MAB : bisector ()
+   z.C      = L.bis.pb
+   L.bisext = T.MAB : bisector_ext ()
+   z.D      = intersection (T.MAB.bc, L.bisext)
+   L.CD     = line: new (z.C,z.D)
+   z.O      = L.CD.mid
+   L.AM     = T.MAB.ab
+   z.E      = z.M : symmetry (z.A)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegment[add=0 and 1](A,M)
+   \tkzDrawSegments[purple](M,C M,D)
+   \tkzDrawCircle[purple](O,C)
+   \tkzDrawSegments(A,B B,M D,B)
+   \tkzDrawPoints(A,B,M,C,D)
+   \tkzLabelPoints[below right](A,B,C,D)
+   \tkzLabelPoints[above](M)
+   \tkzFillAngles[opacity=.4,cyan!20](A,M,B)
+   \tkzFillAngles[opacity=.4,purple!20](B,M,E)
+   \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+   \tkzMarkAngles[mark=|](A,M,C C,M,B)
+   \tkzMarkAngles[mark=||](B,M,D D,M,E)
+\end{tikzpicture} 
+\end{tkzexample}
+
+
+\begin{tkzelements}
+scale=.75
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (6 , 0)
+   z.M  = point: new (5 , 3)
+   T.MAB    = triangle : new (z.M,z.A,z.B)
+   L.bis    = T.MAB : bisector ()
+   z.C  = L.bis.pb
+   L.bisext = T.MAB : bisector_ext ()
+   z.D  = intersection (T.MAB.bc, L.bisext)
+   L.CD = line: new (z.C,z.D)
+   z.O  = L.CD.mid
+   L.AM = T.MAB.ab
+   z.E  = z.M : symmetry (z.A)
+\end{tkzelements}
+
+\hspace*{\fill}  
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegment[add=0 and 1](A,M)
+   \tkzDrawSegments[purple](M,C M,D)
+   \tkzDrawCircle[purple](O,C)
+   \tkzDrawSegments(A,B B,M D,B)
+   \tkzDrawPoints(A,B,M,C,D)
+   \tkzLabelPoints[below right](A,B,C,D)
+   \tkzLabelPoints[above](M)
+   \tkzFillAngles[opacity=.4,cyan!20](A,M,B)
+   \tkzFillAngles[opacity=.4,purple!20](B,M,E)
+   \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+   \tkzMarkAngles[mark=|](A,M,C C,M,B)
+   \tkzMarkAngles[mark=||](B,M,D D,M,E)
+\end{tikzpicture} 
+\hspace*{\fill}
+
+%subsection apollonius_circle (end)
+
+\subsection{Apollonius and circle circumscribed } % (fold)
+\label{sub:apollonius_and_circle_circumscribed}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale =.75
+   z.A   = point: new (0 , 0)
+   z.B   = point: new (6 , 0)
+   L.AB  = line: new (z.A,z.B)
+   z.M   = point: new (5 , 4)
+   T.AMB = triangle: new (z.A,z.M,z.B)
+   z.I   = T.AMB.incenter
+   L.MI  = line: new (z.M,z.I)
+   z.C   = intersection (L.AB , L.MI)
+   z.J   = L.MI: ortho_from (z.M)
+   L.MJ  = line: new (z.M,z.J)
+   z.D   = intersection (L.AB , L.MJ)
+   L.CD  = line: new (z.C,z.D)
+   z.O   = L.CD.mid
+   z.G   = T.AMB.circumcenter
+   C.GA  = circle: new (z.G,z.A)
+   C.OC  = circle: new (z.O,z.C)
+   _,z.N = intersection (C.GA , C.OC)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,M)
+   \tkzDrawCircles[purple](O,C G,A)
+   \tkzDrawSegments[purple](M,D)
+   \tkzDrawSegments(D,B O,G M,C)
+   \tkzDrawSegments[red,dashed](M,N M,O M,G)
+   \tkzDrawPoints(A,B,M,C,D,N,O,G)
+   \tkzLabelPoints[below right](A,B,C,D,N,O,G)
+   \tkzLabelPoints[above](M)
+   \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+   scale =.75
+   z.A   = point: new (0 , 0)
+   z.B   = point: new (6 , 0)
+   z.M   = point: new (5 , 4)
+   T.AMB = triangle: new (z.A,z.M,z.B)
+   L.AB  = T.AMB.ac
+   z.I   = T.AMB.incenter
+   L.MI  = line: new (z.M,z.I)
+   z.C   = intersection (L.AB , L.MI)
+   L.MJ  = L.MI: ortho_from (z.M)
+   z.D   = intersection (L.AB , L.MJ)
+   L.CD  = line: new (z.C,z.D)
+   z.O   = L.CD.mid
+   z.G   = T.AMB.circumcenter
+   C.GA  = circle: new (z.G,z.A)
+   C.OC  = circle: new (z.O,z.C)
+   _,z.N = intersection (C.GA , C.OC)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,M)
+\tkzDrawCircles[purple](O,C G,A)
+\tkzDrawSegments[purple](M,D)
+\tkzDrawSegments(D,B O,G M,C)
+\tkzDrawSegments[red,dashed](M,N M,O M,G)
+\tkzDrawPoints(A,B,M,C,D,N,O,G)
+\tkzLabelPoints[below right](A,B,C,D,N,O,G)
+\tkzLabelPoints[above](M)
+\tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+\end{tikzpicture}
+\hspace*{\fill}
+
+
+%subsection apollonius_and_circle_circumscribed (end)
+%
+\subsection{Apollonius circles in a triangle} % (fold)
+\label{sub:apollonius_circles}
+
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A   = point: new (0 , 0)
+   z.B   = point: new (6 , 0)   
+   z.C   = point: new (4.5 , 1)
+   T.ABC = triangle: new (z.A,z.B,z.C)
+   z.I   = T.ABC.incenter
+   z.O   = T.ABC.circumcenter    
+   L.CI  = line: new (z.C,z.I)
+   z.Cp  = intersection (T.ABC.ab , L.CI)
+   z.x   = L.CI.north_pa
+   L.Cx  = line: new (z.C,z.x)
+   z.R   = intersection (L.Cx,T.ABC.ab)
+   L.CpR = line: new (z.Cp,z.R)
+   z.O1  = L.CpR.mid   
+   L.AI  = line: new (z.A,z.I)
+   z.Ap  = intersection (T.ABC.bc , L.AI)
+   z.y   = L.AI.north_pa
+   L.Ay  = line: new (z.A,z.y)
+   z.S   = intersection (L.Ay,T.ABC.bc)
+   L.ApS = line: new (z.Ap,z.S)
+   z.O2  = L.ApS.mid 
+   L.BI  = line: new (z.B,z.I)
+   z.Bp  = intersection (T.ABC.ac , L.BI)
+   z.z   = L.BI.north_pa
+   L.Bz  = line: new (z.B,z.z)
+   z.T   = intersection (L.Bz,T.ABC.ac)
+   L.Bpt = line: new (z.Bp,z.T)
+   z.O3  = L.Bpt.mid
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[blue!50!black](O1,C' O2,A' O3,B')
+   \tkzDrawSegments[new](B,S C,T A,R)
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawPoints(A,B,C,A',B',C',O,I,R,S,T,O1,O2,O3)
+   \tkzLabelPoints(A,B,C,A',B',C',O,I)
+   \tkzLabelPoints(O1,O2,O3)
+   \tkzDrawCircle[purple](O,A)
+   \tkzDrawLine(O1,O2)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A   = point: new (0 , 0)
+z.B   = point: new (6 , 0)   
+z.C   = point: new (4.5 , 1)
+T.ABC = triangle: new (z.A,z.B,z.C)
+z.I   = T.ABC.incenter
+z.O   = T.ABC.circumcenter    
+L.CI  = line: new (z.C,z.I)
+z.Cp  = intersection (T.ABC.ab , L.CI)
+z.x   = L.CI.north_pa
+L.Cx  = line: new (z.C,z.x)
+z.R   = intersection (L.Cx,T.ABC.ab)
+L.CpR = line: new (z.Cp,z.R)
+z.O1  = L.CpR.mid   
+L.AI  = line: new (z.A,z.I)
+z.Ap  = intersection (T.ABC.bc , L.AI)
+z.y   = L.AI.north_pa
+L.Ay  = line: new (z.A,z.y)
+z.S   = intersection (L.Ay,T.ABC.bc)
+L.ApS = line: new (z.Ap,z.S)
+z.O2  = L.ApS.mid 
+L.BI  = line: new (z.B,z.I)
+z.Bp  = intersection (T.ABC.ac , L.BI)
+z.z   = L.BI.north_pa
+L.Bz  = line: new (z.B,z.z)
+z.T   = intersection (L.Bz,T.ABC.ac)
+L.Bpt = line: new (z.Bp,z.T)
+z.O3  = L.Bpt.mid
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[blue!50!black](O1,C' O2,A' O3,B')
+\tkzDrawSegments[new](B,S C,T A,R)
+\tkzDrawPolygon(A,B,C)
+\tkzDrawPoints(A,B,C,A',B',C',O,I,R,S,T,O1,O2,O3)
+\tkzLabelPoints(A,B,C,A',B',C',O,I)
+\tkzLabelPoints(O1,O2,O3)
+\tkzDrawCircle[purple](O,A)
+\tkzDrawLine(O1,O2)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Apollonius circles in a triangle}
+
+
+% subsection apollonius_circles (end)
+
+\subsection{Archimedes} % (fold)
+\label{sub:archimedes}
+
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.O_1    = point:   new  (0, 0)
+   z.O_2    = point:   new  (0, 1)
+   z.A      = point:   new  (0, 3)
+   z.F      = point:   polar (3, math.pi/6)
+   L        = line:    new   (z.F,z.O_1)
+   C        = circle:  new  (z.O_1,z.A)
+   z.E      = intersection (L,C)
+   T        = triangle: new (z.F,z.E,z.O_2)
+   z.x      = T: parallelogram ()
+   L        = line: new    (z.x,z.O_2)
+   C        = circle: new  (z.O_2,z.A)
+   z.C,z.D  = intersection (L ,C)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O_1,A O_2,A)
+   \tkzDrawSegments[new](O_1,A E,F C,D)
+   \tkzDrawSegments[purple](A,E A,F)
+   \tkzDrawPoints(A,O_1,O_2,E,F,C,D)
+   \tkzLabelPoints(A,O_1,O_2,E,F,C,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+    z.O_1  = point:   new  (0, 0)
+    z.O_2  = point:   new  (0, 1)
+    z.A    = point:   new  (0, 3)
+    z.F    = point:   polar (3, math.pi/6)
+    L  = line:    new   (z.F,z.O_1)
+    C  = circle:  new  (z.O_1,z.A)
+    z.E    = intersection (L,C)
+    T  = triangle: new (z.F,z.E,z.O_2)
+    z.x    = T: parallelogram ()
+    L     = line: new    (z.x,z.O_2)
+    C     = circle: new  (z.O_2,z.A)
+    z.C,z.D   = intersection (L ,C)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O_1,A O_2,A)
+\tkzDrawSegments[new](O_1,A E,F C,D)
+\tkzDrawSegments[purple](A,E A,F)
+\tkzDrawPoints(A,O_1,O_2,E,F,C,D)
+\tkzLabelPoints(A,O_1,O_2,E,F,C,D)
+\end{tikzpicture}
+\hspace*{\fill}
+   %\caption{Archimedes}
+
+
+\subsection{Bankoff circle} % (fold)
+\label{sub:bankoff_circle}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (10 , 0)
+   L.AB     = line : new (z.A,z.B)
+   z.C      = L.AB: gold_ratio ()
+   L.AC     = line : new (z.A,z.C)
+   L.CB     = line : new (z.C,z.B)
+   z.O_0    = L.AB.mid
+   z.O_1    = L.AC.mid
+   z.O_2    = L.CB.mid
+   C.O0B    = circle : new (z.O_0,z.B)
+   C.O1C    = circle : new (z.O_1,z.C)
+   C.O2C    = circle : new (z.O_2,z.B)
+   z.Pp     = C.O0B : midarc (z.B,z.A)
+   z.P      = C.O1C : midarc (z.C,z.A)
+   z.Q      = C.O2C : midarc (z.B,z.C)
+   L.O1O2   = line : new (z.O_1,z.O_2)
+   L.O0O1   = line : new (z.O_0,z.O_1)
+   L.O0O2   = line : new (z.O_0,z.O_2)
+   z.M_0    = L.O1O2 : harmonic_ext (z.C)
+   z.M_1    = L.O0O1 : harmonic_int (z.A)
+   z.M_2    = L.O0O2 : harmonic_int (z.B)
+   L.BP     = line : new (z.B,z.P)
+   L.AQ     = line : new (z.A,z.Q)
+   z.S      = intersection (L.BP,L.AQ)
+   L.PpO0   = line : new (z.Pp,z.O_0)
+   L.PC     = line : new (z.P,z.C)
+   z.Ap     = intersection (L.PpO0,L.PC)
+   L.CS     = line : new (z.C,z.S)
+   C.M1A    = circle : new (z.M_1,z.A)
+   C.M2B    = circle : new (z.M_2,z.B)
+   z.P_0    = intersection (L.CS,C.O0B)
+   z.P_1    = intersection (C.M2B,C.O1C)
+   z.P_2    = intersection (C.M1A,C.O2C)
+   T.P0P1P2 = triangle : new (z.P_0,z.P_1,z.P_2)
+   z.O_4    = T.P0P1P2.circumcenter
+   T.CP1P2  = triangle : new (z.C,z.P_1,z.P_2)
+   z.O_5    = T.CP1P2.circumcenter
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawSemiCircles[teal](O_0,B)
+\tkzDrawSemiCircles[teal,fill=teal!20,opacity=.5](O_1,C O_2,B)
+\tkzDrawCircle[fill=green!10](O_4,P_0)
+\tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C)
+\tkzDrawSegments(A,B O_0,P' B,P A,Q)
+\tkzDrawSegments(P,B Q,O_2 P,O_1)
+\tkzDrawSegments[purple](O_5,P_2 O_5,P_1 O_5,C)
+\tkzDrawPoints(A,B,C,P_0,P_2,P_1,O_0,O_1,O_2,O_4,O_5,Q,P,P',S)
+\tkzLabelPoints[below](A,B,C,O_0,O_1,O_2,P')
+\tkzLabelPoints[above](Q,P)
+\tkzLabelPoints[above right](P_0,P_2,P_1,O_5,O_4,S)
+\begin{scope}[font=\scriptsize]
+  \tkzLabelCircle[above](O_1,C)(120){$(\beta)$}
+  \tkzLabelCircle[above](O_2,B)(70){$(\gamma)$}
+  \tkzLabelCircle[above](O_0,B)(110){$(\alpha)$}
+  \tkzLabelCircle[left](O_4,P_2)(60){$(\delta)$}
+  \tkzLabelCircle[left](O_5,C)(140){$(\epsilon)$}
+\end{scope}
+\end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (10 , 0)
+   L.AB = line : new (z.A,z.B)
+   z.C  = L.AB: gold_ratio ()
+   L.AC = line : new (z.A,z.C)
+   L.CB = line : new (z.C,z.B)
+   z.O_0    = L.AB.mid
+   z.O_1    = L.AC.mid
+   z.O_2    = L.CB.mid
+   C.O0B    = circle : new (z.O_0,z.B)
+   C.O1C    = circle : new (z.O_1,z.C)
+   C.O2C    = circle : new (z.O_2,z.B)
+   z.Pp = C.O0B : midarc (z.B,z.A)
+   z.P  = C.O1C : midarc (z.C,z.A)
+   z.Q  = C.O2C : midarc (z.B,z.C)
+   L.O1O2   = line : new (z.O_1,z.O_2)
+   L.O0O1   = line : new (z.O_0,z.O_1)
+   L.O0O2   = line : new (z.O_0,z.O_2)
+   z.M_0    = L.O1O2 : harmonic_ext (z.C)
+   z.M_1    = L.O0O1 : harmonic_int (z.A)
+   z.M_2    = L.O0O2 : harmonic_int (z.B)
+   L.BP = line : new (z.B,z.P)
+   L.AQ = line : new (z.A,z.Q)
+   z.S  = intersection (L.BP,L.AQ)
+   L.PpO0   = line : new (z.Pp,z.O_0)
+   L.PC = line : new (z.P,z.C)
+   z.Ap = intersection (L.PpO0,L.PC)
+   L.CS = line : new (z.C,z.S)
+   C.M1A    = circle : new (z.M_1,z.A)
+   C.M2B    = circle : new (z.M_2,z.B)
+   z.P_0    = intersection (L.CS,C.O0B)
+   z.P_1    = intersection (C.M2B,C.O1C)
+   z.P_2    = intersection (C.M1A,C.O2C)
+   T.P0P1P2 = triangle : new (z.P_0,z.P_1,z.P_2)
+   z.O_4    = T.P0P1P2.circumcenter
+   T.CP1P2  = triangle : new (z.C,z.P_1,z.P_2)
+   z.O_5    = T.CP1P2.circumcenter
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawSemiCircles[teal](O_0,B)
+\tkzDrawSemiCircles[teal,fill=teal!20,opacity=.5](O_1,C O_2,B)
+\tkzDrawCircle[fill=green!10](O_4,P_0)
+\tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C)
+\tkzDrawSegments(A,B O_0,P' B,P A,Q)
+\tkzDrawSegments(P,B Q,O_2 P,O_1)
+\tkzDrawSegments[purple](O_5,P_2 O_5,P_1 O_5,C)
+\tkzDrawPoints(A,B,C,P_0,P_2,P_1,O_0,O_1,O_2,O_4,O_5,Q,P,P',S)
+\tkzLabelPoints[below](A,B,C,O_0,O_1,O_2,P')
+\tkzLabelPoints[above](Q,P)
+\tkzLabelPoints[above right](P_0,P_2,P_1,O_5,O_4,S)
+\begin{scope}[font=\scriptsize]
+  \tkzLabelCircle[above](O_1,C)(120){$(\beta)$}
+  \tkzLabelCircle[above](O_2,B)(70){$(\gamma)$}
+  \tkzLabelCircle[above](O_0,B)(110){$(\alpha)$}
+  \tkzLabelCircle[left](O_4,P_2)(60){$(\delta)$}
+  \tkzLabelCircle[left](O_5,C)(140){$(\epsilon)$}
+\end{scope}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Bankoff circle}
+
+
+% subsection bankoff_circle (end)
+
+\subsection{Excircles} % (fold)
+\label{sub:excircles}
+
+
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   scale                =  0.7
+   z.A                  = point: new (0,0)
+   z.B                  = point: new (6,0)
+   z.C                  = point: new (.8,4)
+   T                    = triangle: new ( z.A, z.B, z.C)
+   z.K                  = T.centroid
+   z.J_a,z.J_b,z.J_c    = get_points (T: excentral())
+   z.T_a,z.T_b,z.T_c    = get_points (T: extouch())
+   la                   = line: new ( z.A, z.T_a)
+   lb                   = line: new ( z.B, z.T_b)
+   z.G                  = intersection (la,lb)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints[new](J_a,J_b,J_c)
+   \tkzClipBB
+   \tkzDrawCircles[gray](J_a,T_a J_b,T_b J_c,T_c)
+   \tkzDrawLines[add=1 and 1](A,B B,C C,A)
+   \tkzDrawSegments[new](A,T_a B,T_b C,T_c)
+   \tkzDrawSegments[new](J_a,T_a J_b,T_b J_c,T_c)
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawPolygon[new](T_a,T_b,T_c)
+   \tkzDrawPoints(A,B,C,K)
+   \tkzDrawPoints[new](T_a,T_b,T_c)
+   \tkzLabelPoints[below left](A)
+   \tkzLabelPoints[below](B)
+   \tkzLabelPoints[above](C)
+   \tkzLabelPoints[new,below left](T_b)
+   \tkzLabelPoints[new,below right](T_c)
+   \tkzLabelPoints[new,right=6pt](T_a)
+   \tkzMarkRightAngles[fill=gray!15](J_a,T_a,B J_b,T_b,C J_c,T_c,A)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale=0.7
+   z.A    = point: new (0,0)
+   z.B    = point: new (6,0)
+   z.C    = point: new (.8,4)
+   T      = triangle: new ( z.A, z.B, z.C)
+   z.K    = T.centroid
+   z.J_a,z.J_b,z.J_c  = get_points (T: excentral())
+   z.T_a,z.T_b,z.T_c  = get_points (T: extouch())
+   la     = line: new ( z.A, z.T_a)
+   lb     = line: new ( z.B, z.T_b)
+   z.G    = intersection (la,lb)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints[new](J_a,J_b,J_c)
+\tkzClipBB
+\tkzDrawCircles[gray](J_a,T_a J_b,T_b J_c,T_c)
+\tkzDrawLines[add=1 and 1](A,B B,C C,A)
+\tkzDrawSegments[new](A,T_a B,T_b C,T_c)
+\tkzDrawSegments[new](J_a,T_a J_b,T_b J_c,T_c)
+\tkzDrawPolygon(A,B,C)
+\tkzDrawPolygon[new](T_a,T_b,T_c)
+\tkzDrawPoints(A,B,C,K)
+\tkzDrawPoints[new](T_a,T_b,T_c)
+\tkzLabelPoints[below left](A)
+\tkzLabelPoints[below](B)
+\tkzLabelPoints[above](C)
+\tkzLabelPoints[new,below left](T_b)
+\tkzLabelPoints[new,below right](T_c)
+\tkzLabelPoints[new,right=6pt](T_a)
+\tkzMarkRightAngles[fill=gray!15](J_a,T_a,B J_b,T_b,C J_c,T_c,A)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Ex-circles}
+
+
+
+% subsection excircles (end)
+
+\subsection{Harmonic division and bisector} % (fold)
+\label{sub:harmonic_division_and_bisector}
+
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}  
+   scale    =  .75
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (6 , 0)
+   z.M      = point: new (5 , 4)
+   T.AMB    = triangle : new (z.A,z.M,z.B)
+   L.AB     = T.AMB.ac
+   L.bis    = T.AMB : bisector (1)
+   z.C      = L.bis.pb
+   L.bisext = T.AMB : bisector_ext (1)
+   z.D      = intersection (L.bisext,L.AB)
+   L.CD     = line: new (z.C,z.D)
+   z.O      = L.CD.mid
+   L.AM     = line: new (z.A,z.M)
+   L.LL     = L.AM : ll_from (z.B)
+   L.MC     = line: new (z.M,z.C)
+   L.MD     = line: new (z.M,z.D)
+   z.E      = intersection (L.LL,L.MC)
+   z.F      = intersection (L.LL,L.MD)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,M)
+   \tkzDrawCircle[purple](O,C)
+   \tkzDrawSegments[purple](M,E M,D E,F)
+   \tkzDrawSegments(D,B)
+   \tkzDrawPoints(A,B,M,C,D,E,F)
+   \tkzLabelPoints[below right](A,B,C,D,E)
+   \tkzLabelPoints[above](M,F)
+   \tkzFillAngles[opacity=.4,cyan!20](A,M,B B,E,M)
+   \tkzFillAngles[opacity=.4,purple!20](B,M,F M,F,B)
+   \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+   \tkzMarkAngles[mark=||](A,M,E E,M,B B,E,M)
+   \tkzMarkAngles[mark=|](B,M,F M,F,B)
+   \tkzMarkSegments(B,E B,M B,F)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}  
+   scale =.75
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (6 , 0)
+   z.M  = point: new (5 , 4)
+   T.AMB    = triangle : new (z.A,z.M,z.B)
+   L.AB = T.AMB.ac
+   L.bis    = T.AMB : bisector (1)
+   z.C  = L.bis.pb
+   L.bisext = T.AMB : bisector_ext (1)
+   z.D  = intersection (L.bisext,L.AB)
+   L.CD = line: new (z.C,z.D)
+   z.O  = L.CD.mid
+   L.AM = line: new (z.A,z.M)
+   L.LL = L.AM : ll_from (z.B)
+   L.MC = line: new (z.M,z.C)
+   L.MD = line: new (z.M,z.D)
+   z.E  = intersection (L.LL,L.MC)
+   z.F  = intersection (L.LL,L.MD)
+\end{tkzelements}
+
+
+   \hspace*{\fill}   
+   \begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawPolygon(A,B,M)
+  \tkzDrawCircle[purple](O,C)
+  \tkzDrawSegments[purple](M,E M,D E,F)
+  \tkzDrawSegments(D,B)
+  \tkzDrawPoints(A,B,M,C,D,E,F)
+  \tkzLabelPoints[below right](A,B,C,D,E)
+  \tkzLabelPoints[above](M,F)
+  \tkzFillAngles[opacity=.4,cyan!20](A,M,B B,E,M)
+  \tkzFillAngles[opacity=.4,purple!20](B,M,F M,F,B)
+  \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+  \tkzMarkAngles[mark=||](A,M,E E,M,B B,E,M)
+  \tkzMarkAngles[mark=|](B,M,F M,F,B)
+  \tkzMarkSegments(B,E B,M B,F)
+  \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{Harmonic division and bisector}
+
+
+
+
+% subsection harmonic_division_and_bisector (end)
+
+\subsection{Excircle} % (fold)
+\label{sub:excircle}
+
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a     = point:  new (1,2)
+   z.b     = point:  new (5,1)
+   z.c     = point:  new (2,4)
+   T.abc   = triangle: new (z.a,z.b,z.c)
+   z.o,z.p = get_points (T.abc: ex_circle ())
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[add=1 and 1](a,b b,c a,c)
+   \tkzDrawPoints(a,b,c,o,p)
+   \tkzDrawCircles(o,p)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   z.a     = point:  new (1,2)
+   z.b     = point:  new (5,1)
+   z.c     = point:  new (2,4)
+   T.abc   = triangle: new (z.a,z.b,z.c)
+   z.o,z.p = get_points (T.abc: ex_circle ())
+\end{tkzelements}
+
+   \hspace*{\fill}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[add=1 and 1](a,b b,c a,c)
+   \tkzDrawPoints(a,b,c,o,p)
+   \tkzDrawCircles(o,p)
+   \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{Ex-circles}
+
+
+%
+% subsection excircle (end)
+
+\subsection{In/Out of a circle} % (fold)
+\label{sub:in_out_of_a_circle}
+
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale    = 1.25
+   z.A      = point: new (0,0)
+   z.B      = point: new (1,2)
+   z.X      = point: new (-2,2)
+   C        = circle :  new (z.A,z.B)
+   if C:in_out(z.X)
+   then
+  tex.print("In")
+   else
+ tex.print("Out")
+   end
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(A,B)
+   \tkzDrawPoints(A,B,X)
+   \tkzLabelPoints(A,B,X)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 2
+z.A = point: new (0,0)
+z.B = point: new (1,2)
+z.X = point: new (-2,2)
+C = circle :  new (z.A,z.B)
+if C:in_out(z.X)
+then
+   tex.print("In")
+else
+  tex.print("Out")
+end
+  z.M = C: point (math.pi/6)
+\end{tkzelements}
+\hspace*{\fill}\begin{tikzpicture}
+    \tkzGetNodes
+ \tkzDrawCircle(A,B)
+ \tkzDrawPoints(A,B,X,M)
+ \tkzLabelPoints(A,B,X,M)
+\end{tikzpicture}\hspace*{\fill}
+
+% subsection in_out_of_a_circle (end)
+%
+
+\subsection{Orthogonal circle through} % (fold)
+\label{sub:orthogonal_circle_through}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O   = point: new (0,1)
+   z.A   = point: new (1,0)
+   z.z1  = point: new (-1.5,-1.5)
+   z.z2  = point: new (2.5,-1.25)
+   C.OA  = circle: new (z.O,z.A)
+   C     = C.OA: orthogonal_through (z.z1,z.z2)
+   z.c   = C.center
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(O,A)
+   \tkzDrawCircle[new](c,z1)
+   \tkzDrawPoints[new](O,A,z1,z2,c)
+   \tkzLabelPoints[right](O,A,z1,z2,c)
+\end{tikzpicture}
+\end{tkzexample}%
+
+\begin{tkzelements}
+   z.O   = point: new (0,1)
+   z.A   = point: new (1,0)
+   z.z1  = point: new (-1.5,-1.5)
+   z.z2  = point: new (2.5,-1.25)
+   C.OA  = circle: new (z.O,z.A)
+   C = C.OA: orthogonal_through (z.z1,z.z2)
+   z.c   = C.center
+\end{tkzelements}
+
+   \hspace*{\fill}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(O,A)
+   \tkzDrawCircle[orange](c,z1)
+   \tkzDrawPoints[orange](O,A,z1,z2,c)
+   \tkzLabelPoints[right](O,A,z1,z2,c)
+   \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{Orthogonal circle through}
+
+
+% subsection orthogonal_circle_through (end)
+
+\subsection{Devine ratio} % (fold)
+\label{sub:devine_ratio}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+z.A         = point: new (0 , 0)
+z.B         = point: new (8 , 0)
+L.AB        = line: new (z.A,z.B)
+z.C         = L.AB: gold_ratio ()
+L.AC        = line: new (z.A,z.C)
+z.O_1       = L.AC.mid
+z.G,z.H     = L.AB: square ()
+z.E,z.F     = L.AC: square ()
+L.CB        = line: new (z.C,z.B)
+z.O_2       = L.CB.mid
+z.O_0       = L.AB.mid
+L.BE        = line: new (z.B,z.E)
+L.GH        = line: new (z.G,z.H)
+z.K         = intersection (L.BE,L.GH)
+C0          = circle: new (z.O_0,z.B)
+z.R,_       = intersection (L.BE,C0)
+C2          = circle: new (z.O_2,z.B)
+z.S,_       = intersection (L.BE,C2)
+L.AR        = line:   new (z.A,z.R)
+C1          = circle: new (z.O_1,z.C)
+_,z.T       = intersection (L.AR,C1)
+L.BG        = line: new (z.B,z.G)
+z.L         = intersection (L.AR,L.BG)
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(A,C,E,F A,B,G,H)
+\tkzDrawCircles(O_1,C O_2,B O_0,B)
+\tkzDrawSegments(H,C B,K A,L)
+\tkzDrawPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
+\tkzLabelPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A = point: new (0 , 0)
+z.B = point: new (8 , 0)
+L.AB    = line: new (z.A,z.B)
+z.C = L.AB: gold_ratio ()
+L.AC    = line: new (z.A,z.C)
+z.O_1   = L.AC.mid
+z.G,z.H = L.AB: square ()
+z.E,z.F = L.AC: square ()
+L.CB    = line: new (z.C,z.B)
+z.O_2   = L.CB.mid
+z.O_0   = L.AB.mid
+L.BE    = line: new (z.B,z.E)
+L.GH    = line: new (z.G,z.H)
+z.K = intersection (L.BE,L.GH)
+C0  = circle: new (z.O_0,z.B)
+z.R,_   = intersection (L.BE,C0)
+C2  = circle: new (z.O_2,z.B)
+z.S,_   = intersection (L.BE,C2)
+L.AR    = line:   new (z.A,z.R)
+C1  = circle: new (z.O_1,z.C)
+_,z.T   = intersection (L.AR,C1)
+L.BG    = line: new (z.B,z.G)
+z.L = intersection (L.AR,L.BG)
+\end{tkzelements}
+
+   \hspace*{\fill}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(A,C,E,F A,B,G,H)
+   \tkzDrawCircles(O_1,C O_2,B O_0,B)
+   \tkzDrawSegments(H,C B,K A,L)
+   \tkzDrawPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
+   \tkzLabelPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
+   \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{Devine or gold ratio}
+
+
+
+% subsection devine_ratio (end)
+
+\subsection{Director circle} % (fold)
+\label{sub:director_circle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+scale    = .5
+z.O      = point: new (0 , 0)
+z.F1     = point: new (4 , 0)
+z.F2     = point: new (-4 , 0)
+z.H      = point: new (4*math.sqrt(2) , 0)
+E        = ellipse: foci (z.F2,z.F1,z.H)
+a,b      = E.Rx, E.Ry
+z.A      = E.covertex
+T        = triangle: new (z.H,z.O,z.A)
+z.P      = T: parallelogram ()
+C        = circle: new (z.O,z.P)
+z.L      = C: point (2)
+L.J,L.K  = E: tangent_from (z.L)
+z.J      = L.J.pb
+z.K      = L.K.pb
+set_lua_to_tex {'a','b'}
+\end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPoints(F1,F2,O)
+\tkzDrawCircles[teal](O,P)
+\tkzDrawPolygon(H,O,A,P)
+\tkzDrawEllipse[red](O,\a,\b,0)
+\tkzDrawSegments[orange](O,P O,L L,J L,K)
+\tkzDrawPoints(F1,F2,O,H,A,P,L,J,K)
+\tkzLabelPoints(F1,F2,O,H,A,P,L,J,K)
+\tkzMarkRightAngles(A,P,H J,L,K)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.O   = point: new (0 , 0)
+z.F1  = point: new (4 , 0)
+z.F2  = point: new (-4 , 0)
+z.H   = point: new (4*math.sqrt(2) , 0)
+E     = ellipse: foci (z.F2,z.F1,z.H)
+a,b   = E.Rx, E.Ry
+z.A   = E.covertex
+T     = triangle: new (z.H,z.O,z.A)
+z.P   = T: parallelogram ()
+C     = circle: new (z.O,z.P)
+z.L   = C: point (2)
+L.J,L.K  = E: tangent_from (z.L)
+z.J      = L.J.pb
+z.K      = L.K.pb
+set_lua_to_tex {'a','b'}
+\end{tkzelements}
+
+
+\hspace*{\fill} 
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(F1,F2,O)
+\tkzDrawCircles[teal](O,P)
+\tkzDrawPolygon(H,O,A,P)
+\tkzDrawEllipse[red](O,\a,\b,0)
+\tkzDrawSegments[orange](O,P O,L L,J L,K)
+\tkzDrawPoints(F1,F2,O,H,A,P,L,J,K)
+\tkzLabelPoints(F1,F2,O,H,A,P,L,J,K)
+\tkzMarkRightAngles(A,P,H J,L,K)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Director circle}
+% subsection director_circle (end)
+
+\subsection{Distance} % (fold)
+\label{sub:distance}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point : new (0 , 0)
+   z.B      = point : new (4 , 3)
+   z.C      = point : new (2 , 5)
+   L.AB     = line : new (z.A,z.B)
+   d        = L.AB : distance (z.C)
+   l        = L.AB.length
+   z.H      = L.AB : projection (z.C)
+   set_lua_to_tex{'d','l'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,B C,H)
+   \tkzDrawPoints(A,B,C,H)
+   \tkzLabelPoints(A,B,C,H)
+   \tkzLabelSegment[above left,draw](C,H){$CH = \d$}
+   \tkzLabelSegment[below left,draw](C,H){$AB = \l$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A    = point : new (0 , 0)
+z.B    = point : new (4 , 3)
+z.C    = point : new (2 , 5)
+L.AB   = line : new (z.A,z.B)
+d      = L.AB : distance (z.C)
+l      = L.AB.length
+z.H    = L.AB : projection (z.C)
+set_lua_to_tex{'d','l'}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B C,H)
+\tkzDrawPoints(A,B,C,H)
+\tkzLabelPoints(A,B,C,H)
+\tkzLabelSegment[above left,draw](C,H){$CH = \d$}
+\tkzLabelSegment[below left,draw](C,H){$AB = \l$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Distance to a line}
+
+
+
+% subsection distance (end)
+
+\subsection{Gold division} % (fold)
+\label{sub:gold_division}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point:  new (0,0)
+   z.B      = point:  new (2.5,0)
+   L.AB     = line:   new (z.A,z.B)
+   C.AB     = circle: new (z.A,z.B)
+   C.BA     = circle: new (z.B,z.A)
+   z.J      = L.AB: midpoint ()
+   L.JB     = line:new (z.J,z.B)
+   z.F,z.E  = intersection (C.AB , C.BA)
+   z.I,_    = intersection (L.AB , C.BA)
+   z.K      = L.JB : midpoint ()
+   z.k      = L.JB: ortho_from (z.K)
+   L.Kk     = line:new (z.K,z.k)
+   _,z.G    = intersection (L.Kk,C.BA)
+   L.EG     = line:new (z.E,z.G)
+   z.C      = intersection  (L.EG,L.AB)
+   z.O      = C.AB: antipode (z.B)
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+   \tkzDrawArc[delta=5](O,B)(G)
+   \tkzDrawCircles(A,B B,A)
+   \tkzDrawSegments(A,E B,E O,I)
+   \tkzDrawSegments[purple](J,E A,G G,I K,G E,G)
+   \tkzMarkSegments[mark=s||](A,E B,E O,A)
+   \tkzDrawPoints(A,B,C,E,I,J,G,O,K)
+   \tkzLabelPoints(A,B,C,E,I,J,G,O,K)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A     = point:  new (0,0)
+z.B     = point:  new (2.5,0)
+L.AB    = line:   new (z.A,z.B)
+C.AB    = circle: new (z.A,z.B)
+C.BA    = circle: new (z.B,z.A)
+z.J     = L.AB: midpoint ()
+L.JB    = line:new (z.J,z.B)
+z.F,z.E = intersection (C.AB , C.BA)
+z.I,_   = intersection (L.AB , C.BA)
+z.K     = L.JB : midpoint ()
+L.mediator  = L.JB: mediator ()
+z.G   = intersection (L.mediator,C.BA)
+L.EG    = line:new (z.E,z.G)
+z.C     = intersection  (L.EG,L.AB)
+z.O     = C.AB: antipode (z.B)
+\end{tkzelements}
+
+   \hspace*{\fill}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawArc[delta=5](O,B)(G)
+   \tkzDrawCircles(A,B B,A)
+   \tkzDrawSegments(A,E B,E O,I)
+   \tkzDrawSegments[purple](J,E A,G G,I K,G E,G)
+   \tkzMarkSegments[mark=s||](A,E B,E O,A)
+   \tkzDrawPoints(A,B,C,E,I,J,G,O,K)
+   \tkzLabelPoints(A,B,C,E,I,J,G,O,K)
+   \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{gold division}
+
+
+
+
+% subsection gold_division (end)
+
+\subsection{Ellipse} % (fold)
+\label{sub:ellipse}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.C       = point: new (3 , 2)
+   z.A       = point: new (5 , 1)
+   L.CA      = line : new (z.C,z.A)
+   z.b       = L.CA.north_pa
+   L         = line : new (z.C,z.b)
+   z.B       = L : point (0.5)
+   E         = ellipse: new (z.C,z.A,z.B)
+   a         = E.Rx
+   b         = E.Ry
+   slope     = math.deg(E.slope)
+   set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[teal](C,A)
+   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawPoints(C,A,B,b)
+   \tkzLabelPoints(C,A,B)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.C  = point: new (3 , 2)
+z.A  = point: new (5 , 1)
+L.CA = line : new (z.C,z.A)
+z.b  = L.CA.north_pa
+L    = line : new (z.C,z.b)
+z.B  = L : point (0.5)
+E    = ellipse: new (z.C,z.A,z.B)
+a    = E.Rx
+b    = E.Ry
+slope    = math.deg(E.slope)
+set_lua_to_tex {'a','b','slope'}
+\end{tkzelements}
+
+   \hspace*{\fill}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[teal](C,A)
+   \tkzDrawEllipse[red](C,\a,\b,\slope)
+   \tkzDrawPoints(C,A,B,b)
+   \tkzLabelPoints(C,A,B)
+   \end{tikzpicture}
+   \hspace*{\fill}
+   %\caption{Ellipse}
+
+% subsection ellipse (end)
+
+\subsection{Ellipse with radii} % (fold)
+\label{sub:ellipse_with_radii}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+z.C      = point: new (0 , 4)
+z.B      = point: new (4 , 0)
+z.D      = point: new (2 , 6)
+b        = math.sqrt(8)
+a        = math.sqrt(32)
+ang      = math.deg(math.pi/4)
+E        = ellipse: radii (z.C,a,b,math.pi/4)
+z.V      = E : point (0)
+z.CoV    = E : point (math.pi/2)
+set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawEllipse[blue](C,\a,\b,\ang)
+\tkzDrawPoints(C,V,CoV)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.C    = point: new (0 , 4)
+z.B    = point: new (4 , 0)
+z.D    = point: new (2 , 6)
+b  = math.sqrt(8)
+a  = math.sqrt(32)
+ang    = math.deg(math.pi/4)
+E  = ellipse: radii (z.C,a,b,math.pi/4)
+z.V    = E : point (0)
+z.CoV  = E : point (math.pi/2)
+set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawEllipse[blue](C,\a,\b,\ang)
+\tkzDrawPoints(C,V,CoV)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Ellipse with radii}
+% subsection ellipse_with_radii (end)
+
+\subsection{Ellipse\_with\_foci} % (fold)
+\label{sub:ellipse_with_foci}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   local e
+   e           = .8
+   z.A         = point: new (2 , 3)
+   z.B         = point: new (5 , 4)
+   z.K         = point: new (6, 7)  
+   L.AB        = line: new (z.A,z.B)
+   z.C         = L.AB.mid
+   c           = point.abs(z.B-z.C)
+   a           = c/e
+   b           = math.sqrt (a^2-c^2)  
+   z.V         = z.C + a*(z.B-z.C)/point.abs(z.B-z.C)   
+   E           = ellipse: foci (z.A,z.B,z.V)
+   z.cV        = E.covertex 
+   ang         = math.deg(E.slope)
+   L.ta,L.tb   = E: tangent_from (z.K)
+   z.F         = L.ta.pb
+   z.G         = L.tb.pb
+   set_lua_to_tex{'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints(A,B,C,K,F,G,V,cV)
+   \tkzLabelPoints(A,B,C,K,F,G,V,cV)
+   \tkzDrawEllipse[teal](C,\a,\b,\ang)
+   \tkzDrawLines(K,F K,G)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+local e
+e           = .8
+z.A         = point: new (2 , 3)
+z.B         = point: new (5 , 4)
+z.K         = point: new (6, 7)  
+L.AB        = line: new (z.A,z.B)
+z.C         = L.AB.mid
+c           = point.abs(z.B-z.C)
+a           = c/e
+b           = math.sqrt (a^2-c^2)  
+z.V         = z.C + a*(z.B-z.C)/point.abs(z.B-z.C)   
+E           = ellipse: foci (z.A,z.B,z.V)
+z.cV        = E.covertex 
+ang         = math.deg(E.slope)
+L.ta,L.tb   = E: tangent_from (z.K)
+z.F         = L.ta.pb
+z.G         = L.tb.pb
+set_lua_to_tex{'a','b','ang'}
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawPoints(A,B,C,K,F,G,V,cV)
+  \tkzLabelPoints(A,B,C,K,F,G,V,cV)
+  \tkzDrawEllipse[teal](C,\a,\b,\ang)
+  \tkzDrawLines(K,F K,G)
+\end{tikzpicture}
+ \hspace*{\fill}
+  %\caption{Ellipse with foci}
+
+
+
+% subsection ellipse_with_foci (end)
+
+\subsection{Euler relation} % (fold)
+\label{sub:euler_relation}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale          =  .75
+   z.A            = point: new (0 , 0)
+   z.B            = point: new (5 , 0)
+   z.C            = point: new (-.4 , 4)
+   T.ABC          = triangle: new (z.A,z.B,z.C)
+   z.J,z.K        = get_points(T.ABC: ex_circle (2))
+   z.X ,z.Y,z.K   = T.ABC : projection (z.J)
+   z.I,z.H        = get_points(T.ABC : in_circle())
+   z.O            = T.ABC.circumcenter
+   C.OA           = circle : new (z.O,z.A)
+   T.IBA          = triangle: new (z.I,z.B,z.A)
+   z.w            = T.IBA.circumcenter
+   L.Ow           = line : new (z.O,z.w)
+   _,z.E          = intersection (L.Ow, C.OA)
+\end{tkzelements}
+   \begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawArc(J,X)(Y)
+   \tkzDrawCircles(I,H O,A)
+   \tkzDrawCircle[red](w,I)
+   \tkzDrawLines(Y,C A,B X,C E,w E,B)
+   \tkzDrawSegments[blue](J,C J,K I,H I,O w,B)
+   \tkzDrawPoints(A,B,C,I,J,E,w,H,K,O)
+   \tkzLabelPoints(A,B,C,J,I,w,H,K,E,O)
+   \tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J)
+   \end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A   = point: new (0 , 0)
+z.B   = point: new (5 , 0)
+   z.C    = point: new (-.4 , 4)
+T.ABC     = triangle: new (z.A,z.B,z.C)
+z.J,z.K   = get_points(T.ABC: ex_circle (2))
+z.X ,z.Y,z.K  = T.ABC : projection (z.J)
+z.I,z.H   = get_points(T.ABC : in_circle())
+z.O   = T.ABC.circumcenter
+C.OA      = circle : new (z.O,z.A)
+T.IBA     = triangle: new (z.I,z.B,z.A)
+z.w   = T.IBA.circumcenter
+L.Ow      = line : new (z.O,z.w)
+_,z.E     = intersection (L.Ow, C.OA)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawArc(J,X)(Y)
+\tkzDrawCircles(I,H O,A)
+\tkzDrawCircle[red](w,I)
+\tkzDrawLines(Y,C A,B X,C E,w E,B)
+\tkzDrawSegments[blue](J,C J,K I,H I,O w,B)
+\tkzDrawPoints(A,B,C,I,J,E,w,H,K,O)
+\tkzLabelPoints(A,B,C,J,I,w,H,K,E,O)
+\tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Euler relation}
+% subsection euler_relation (end)
+
+\subsection{Euler line} % (fold)
+\label{sub:euler_line}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A           = point: new (0 , 0)
+   z.B           = point: new (6 , 0)
+   z.C           = point: new (1.5 , 3.5)
+   T.ABC         = triangle: new (z.A,z.B,z.C)
+   z.O           = T.ABC.circumcenter
+   z.G           = T.ABC.centroid
+   z.N           = T.ABC. eulercenter
+   z.H           = T.ABC. orthocenter
+   z.P,z.Q,z.R   = get_points (T.ABC: orthic())
+   z.K,z.I,z.J   = get_points (T.ABC: medial ())
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[blue](O,H)
+   \tkzDrawCircle[red](N,I)
+   \tkzDrawCircles[teal](O,A)
+   \tkzDrawSegments(A,P B,Q C,R)
+   \tkzDrawSegments[red](A,I B,J C,K)
+   \tkzDrawPolygons(A,B,C)
+   \tkzDrawPoints(A,B,C,N,I,J,K,O,P,Q,R,H,G)
+   \tkzLabelPoints(A,B,C,I,J,K,P,Q,R,H)
+   \tkzLabelPoints[below](N,O,G)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+ scale =1
+ z.A    = point: new (0 , 0)
+ z.B    = point: new (6 , 0)
+ z.C    = point: new (1.5 , 3.5)
+ T.ABC  = triangle: new (z.A,z.B,z.C)
+ z.O    = T.ABC.circumcenter
+ z.G    = T.ABC.centroid
+ z.N    = T.ABC. eulercenter
+ z.H    = T.ABC. orthocenter
+ z.P,z.Q,z.R    = get_points (T.ABC: orthic())
+ z.K,z.I,z.J    = get_points (T.ABC: medial ())
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines[blue](O,H)
+\tkzDrawCircle[red](N,I)
+\tkzDrawCircles[teal](O,A)
+\tkzDrawSegments(A,P B,Q C,R)
+\tkzDrawSegments[red](A,I B,J C,K)
+\tkzDrawPolygons(A,B,C)
+\tkzDrawPoints(A,B,C,N,I,J,K,O,P,Q,R,H,G)
+\tkzLabelPoints(A,B,C,I,J,K,P,Q,R)
+\tkzLabelPoints[below](N,O,G,H)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Euler line}
+% subsection euler_line (end)
+
+\subsection{External angle} % (fold)
+\label{sub:external_angle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale =.8
+   z.A    = point: new (0 , 0)
+   z.B    = point: new (5 , 0)
+   z.C    = point: new (-2 , 4)
+   T.ABC  = triangle: new (z.A,z.B,z.C)
+   T.ext  = T.ABC: excentral ()
+   z.O    = T.ABC.circumcenter
+   z.D    = intersection (T.ext.ab,T.ABC.ab)
+   z.E    = z.C: symmetry (z.B)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawLine[purple,add=0 and .5](B,C)
+   \tkzDrawSegment[purple](A,D)
+   \tkzDrawSegment[orange](C,D)
+   \tkzFillAngles[purple!30,opacity=.2](D,C,A E,C,D)
+   \tkzMarkAngles[mark=|](D,C,A E,C,D)
+   \tkzDrawPoints(A,...,D)
+   \tkzLabelPoints[above](C)
+   \tkzLabelPoints(A,B,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale    = .8
+z.A      = point: new (0 , 0)
+z.B      = point: new (5 , 0)
+z.C      = point: new (-2 , 4)
+T.ABC    = triangle: new (z.A,z.B,z.C)
+T.ext    = T.ABC: excentral ()
+z.O      = T.ABC.circumcenter
+z.D      = intersection (T.ext.ab,T.ABC.ab)
+z.E      = z.C: symmetry (z.B)
+\end{tkzelements}
+
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawLine[purple,add=0 and .5](B,C)
+\tkzDrawSegment[purple](A,D)
+\tkzDrawSegment[orange](C,D)
+\tkzFillAngles[purple!30,opacity=.2](D,C,A E,C,D)
+\tkzMarkAngles[mark=|](D,C,A E,C,D)
+\tkzDrawPoints(A,...,D)
+\tkzLabelPoints[above](C)
+\tkzLabelPoints(A,B,D)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{External angle}
+% subsection external_angle (end)
+
+\subsection{Internal angle} % (fold)
+\label{sub:internal_angle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale =  .8
+   z.A   = point: new (0 , 0)
+   z.B   = point: new (6 , 0)
+   z.C   = point: new (1 , 5)
+   T     = triangle: new (z.A,z.B,z.C)
+   z.I   = T.incenter
+   L.AI  = line: new (z.A,z.I)
+   z.D   = intersection (L.AI, T.bc)
+   L.LL  = T.ab: ll_from (z.C)
+   L.AD  = line: new (z.A,z.D)
+   z.E   = intersection (L.LL,L.AD)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawLine[purple](C,E)
+   \tkzDrawSegment[purple](A,E)
+   \tkzFillAngles[purple!30,opacity=.4](B,A,C C,E,D) 
+   \tkzMarkAngles[mark=|](B,A,D D,A,C C,E,D)    
+   \tkzDrawPoints(A,...,E) 
+   \tkzLabelPoints(A,B)   
+   \tkzLabelPoints[above](C,D,E) 
+   \tkzMarkSegments(A,C C,E)   
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale =.8
+z.A = point: new (0 , 0)
+z.B = point: new (6 , 0)
+z.C = point: new (1 , 5)
+T   = triangle: new (z.A,z.B,z.C)
+z.I = T.incenter
+L.AI    = line: new (z.A,z.I)
+z.D = intersection (L.AI, T.bc)
+L.LL    = T.ab: ll_from (z.C)
+L.AD    = line: new (z.A,z.D)
+z.E = intersection (L.LL,L.AD)
+\end{tkzelements}
+
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawLine[purple](C,E)
+\tkzDrawSegment[purple](A,E)
+\tkzFillAngles[purple!30,opacity=.4](B,A,C C,E,D) 
+\tkzMarkAngles[mark=|](B,A,D D,A,C C,E,D)    
+\tkzDrawPoints(A,...,E) 
+\tkzLabelPoints(A,B)   
+\tkzLabelPoints[above](C,D,E) 
+\tkzMarkSegments(A,C C,E)   
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Internal angle}
+%subsection internal_angle (end)
+
+\subsection{Feuerbach theorem} % (fold)
+\label{sub:nine_points}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale     =  1.5
+   z.A       = point: new (0 , 0)
+   z.B       = point: new (5 , -.5)
+   z.C       = point: new (-.5 , 3)
+   T.ABC     = triangle: new (z.A,z.B,z.C)
+   z.O       = T.ABC.circumcenter
+   z.N       = T.ABC.eulercenter
+   z.I,z.K   = get_points(T.ABC: in_circle())
+   z.H       = T.ABC.ab : projection (z.I)
+   z.Ap,
+   z.Bp,
+   z.Cp      = get_points (T.ABC : medial ())
+   C.IH      = circle:new (z.I,z.H)
+   C.NAp     = circle:new (z.N,z.Ap)
+   C.OA      = circle:new (z.O,z.A)
+   z.U       = C.OA.south
+   z.L       = C.NAp.south
+   z.M       = C.NAp.north
+   z.X       = T.ABC.ab: projection (z.C)
+   L.CU      = line: new (z.C,z.U)
+   L.ML      = line: new (z.M,z.L)
+   z.P       = L.CU: projection (z.A)
+   z.Q       = L.CU: projection (z.B)
+   L.LH      = line: new (z.L,z.H)
+   z.F       = intersection (L.LH,C.IH) -- feuerbach
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLine(L,F)
+   \tkzDrawCircle[red](N,A')
+   \tkzDrawCircle[blue](I,H)
+   \tkzDrawCircles[teal](O,A L,C')
+   \tkzDrawSegments(M,L B,U Q,C C,X A,P B,Q)
+   \tkzDrawPolygons(A,B,C A',B',C')
+   \tkzDrawPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
+   \tkzLabelPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale  =  1
+z.A    = point: new (0 , 0)
+z.B    = point: new (5 , -.5)
+z.C    = point: new (-.5 , 3)
+T.ABC  = triangle: new (z.A,z.B,z.C)
+z.O    = T.ABC.circumcenter
+z.N    = T.ABC.eulercenter
+z.I,z.K    = get_points(T.ABC: in_circle())
+z.H = T.ABC.ab : projection (z.I)
+z.Ap,z.Bp,z.Cp = get_points (T.ABC : medial ())
+C.IH   = circle:new (z.I,z.H)
+C.NAp  = circle:new (z.N,z.Ap)
+C.OA   = circle:new (z.O,z.A)
+z.U    = C.OA.south
+z.L    = C.NAp.south
+z.M    = C.NAp.north
+z.X    = T.ABC.ab: projection (z.C)
+L.CU   = line: new (z.C,z.U)
+L.ML   = line: new (z.M,z.L)
+z.P    = L.CU: projection (z.A)
+z.Q    = L.CU: projection (z.B)
+L.LH   = line: new (z.L,z.H)
+z.F  = intersection (L.LH,C.IH) -- feuerbach
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}[rotate=90]
+\tkzGetNodes
+\tkzDrawLine(L,F)
+\tkzDrawCircle[red](N,A')
+\tkzDrawCircle[blue](I,H)
+\tkzDrawCircles[teal](O,A L,C')
+\tkzDrawSegments(M,L B,U Q,C C,X A,P B,Q)
+\tkzDrawPolygons(A,B,C A',B',C')
+\tkzDrawPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
+\tkzLabelPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
+\end{tikzpicture}   
+\hspace*{\fill}
+%\caption{Feuerbach theorem}
+
+
+
+
+% subsection nine_points (end)
+
+\subsection{Gold ratio with segment} % (fold)
+\label{sub:gold_ratio_with_segment}
+
+ \begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (8 , 0)
+   L.AB     = line: new (z.A,z.B)
+   z.X,z.Y  = L.AB: square ()
+   L.BX     = line: new (z.B,z.X)
+   z.M      = L.BX.mid
+   C.MA     = circle: new (z.M,z.A)
+   _,z.K    = intersection (L.BX,C.MA)
+   L.AK     = line: new (z.Y,z.K)
+   z.C      = intersection (L.AK,L.AB)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,B X,K)
+   \tkzDrawLine[teal](Y,K)
+   \tkzDrawPoints(A,B,C,X,Y,M,K)
+   \tkzDrawArc[delta=20](M,A)(K)
+   \tkzLabelPoints(A,B,C)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.A = point: new (0 , 0)
+z.B = point: new (8 , 0)
+L.AB    = line: new (z.A,z.B)
+z.X,z.Y = L.AB: square ()
+L.BX    = line: new (z.B,z.X)
+z.M = L.BX.mid
+C.MA    = circle: new (z.M,z.A)
+_,z.K   = intersection (L.BX,C.MA)
+L.AK    = line: new (z.Y,z.K)
+z.C = intersection (L.AK,L.AB)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B X,K)
+\tkzDrawLine[teal](Y,K)
+\tkzDrawPoints(A,B,C,X,Y,M,K)
+\tkzDrawArc[delta=20](M,A)(K)
+\tkzLabelPoints(A,B,C)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Gold ration with a segment}
+%subsection gold_ratio_with_segment (end)
+
+\subsection{Gold Arbelos} % (fold)
+\label{sub:gold_arbelos}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale    = .6
+   z.A      = point: new (0 , 0)
+   z.C      = point: new (6 , 0)
+   L.AC     = line: new (z.A,z.C)
+   z.x,z.y  = L.AC: square ()
+   z.O_1    = L.AC . mid
+   C        = circle: new (z.O_1,z.x)
+   z.B      = intersection (L.AC,C)
+   L.CB     = line: new (z.C,z.B)
+   z.O_2    = L.CB.mid
+   L.AB     = line: new (z.A,z.B)
+   z.O_0    = L.AB.mid
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O_1,C O_2,B O_0,B)
+   \tkzDrawPoints(A,C,B,O_1,O_2,O_0)
+   \tkzLabelPoints(A,C,B)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale    = .4
+z.A  = point: new (0 , 0)
+z.C  = point: new (6 , 0)
+L.AC = line: new (z.A,z.C)
+z.x,z.y  = L.AC: square ()
+z.O_1    = L.AC . mid
+C    = circle: new (z.O_1,z.x)
+z.B  = intersection (L.AC,C)
+L.CB = line: new (z.C,z.B)
+z.O_2    = L.CB.mid
+L.AB = line: new (z.A,z.B)
+z.O_0    = L.AB.mid
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O_1,C O_2,B O_0,B O_1,x)
+\tkzDrawPoints(A,C,B,O_1,O_2,O_0,x)
+\tkzLabelPoints(A,C,B)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Gold Arbelos}
+% subsection gold_arbelos (end)
+
+\subsection{Harmonic division v1} % (fold)
+\label{sub:harmonic_division_v1}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale=.75
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (4 , 0)
+   z.D  = point: new (12,0)
+   L.AB = line : new (z.A,z.B)
+   z.X  = L.AB.north_pa
+   L.XB = line : new (z.X,z.B)
+   z.E  = L.XB.mid
+   L.DE = line : new (z.D,z.E)
+   L.XA = line : new (z.X,z.A)
+   z.F  = intersection (L.DE,L.XA)
+   L.AE = line : new (z.A,z.E)
+   L.BF = line : new (z.B,z.F)
+   z.G  = intersection (L.AE,L.BF)
+   L.XG = line : new (z.X,z.G)
+z.C  = intersection (L.XG,L.AB)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDefPoints{0/0/A,4/0/B}
+   \tkzDefPoints{2/2/G}
+   \tkzDefLine[parallel=through B,K=.5](A,G) \tkzGetPoint{E}
+   \tkzInterLL(G,E)(A,B)   \tkzGetPoint{D}
+   \tkzDefPointBy[symmetry= center B](E) \tkzGetPoint{F}
+   \tkzInterLL(G,F)(A,B)   \tkzGetPoint{C}
+   \tkzDrawLines(A,D A,G F,E G,F G,D)
+   \tkzDrawPoints(A,B,G,E,F,C,D)
+   \tkzLabelPoints(A,B,G,E,F,C,D)
+   \tkzMarkSegments(F,B B,E)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale=.75
+z.A  = point: new (0 , 0)
+z.B  = point: new (4 , 0)
+z.D  = point: new (12,0)
+L.AB = line : new (z.A,z.B)
+z.X  = L.AB.north_pa
+L.XB = line : new (z.X,z.B)
+z.E  = L.XB.mid
+L.DE = line : new (z.D,z.E)
+L.XA = line : new (z.X,z.A)
+z.F  = intersection (L.DE,L.XA)
+L.AE = line : new (z.A,z.E)
+L.BF = line : new (z.B,z.F)
+z.G  = intersection (L.AE,L.BF)
+L.XG = line : new (z.X,z.G)
+z.C  = intersection (L.XG,L.AB)
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDefPoints{0/0/A,4/0/B}
+\tkzDefPoints{2/2/G}
+\tkzDefLine[parallel=through B,K=.5](A,G) \tkzGetPoint{E}
+\tkzInterLL(G,E)(A,B)   \tkzGetPoint{D}
+\tkzDefPointBy[symmetry= center B](E) \tkzGetPoint{F}
+\tkzInterLL(G,F)(A,B)   \tkzGetPoint{C}
+\tkzDrawLines(A,D A,G F,E G,F G,D)
+\tkzDrawPoints(A,B,G,E,F,C,D)
+\tkzLabelPoints(A,B,G,E,F,C,D)
+\tkzMarkSegments(F,B B,E)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Harmonic division V1}
+% subsection harmonic_division_v1 (end)
+
+\subsection{Harmonic division v2} % (fold)
+\label{sub:harmonic_division_v2}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale    = .5
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (6 , 0)
+   z.D      = point: new (12 , 0)
+   L.AB     = line: new (z.A,z.B)
+   z.X      = L.AB.north_pa
+   L.XB     = line: new (z.X,z.B)
+   z.E      = L.XB.mid
+   L.ED     = line: new (z.E,z.D)
+   L.AX     = line: new (z.A,z.X)
+   L.AE     = line: new (z.A,z.E)
+   z.F      = intersection (L.ED,L.AX)
+   L.BF     = line: new (z.B,z.F)
+   z.G      = intersection (L.AE,L.BF)
+   L.GX     = line: new (z.G,z.X)
+   z.C      = intersection (L.GX,L.AB)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines(A,D A,E B,F D,F X,A X,B X,C)
+   \tkzDrawPoints(A,...,G,X)
+   \tkzLabelPoints(A,...,G,X)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.A    = point: new (0 , 0)
+z.B    = point: new (6 , 0)
+z.D    = point: new (12 , 0)
+L.AB   = line: new (z.A,z.B)
+z.X    = L.AB.north_pa
+L.XB   = line: new (z.X,z.B)
+z.E    = L.XB.mid
+L.ED   = line: new (z.E,z.D)
+L.AX   = line: new (z.A,z.X)
+L.AE   = line: new (z.A,z.E)
+z.F    = intersection (L.ED,L.AX)
+L.BF   = line: new (z.B,z.F)
+z.G    = intersection (L.AE,L.BF)
+L.GX   = line: new (z.G,z.X)
+z.C    = intersection (L.GX,L.AB)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,D A,E B,F D,F X,A X,B X,C)
+\tkzDrawPoints(A,...,G,X)
+\tkzLabelPoints(A,...,G,X)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Harmonic division V2}
+% subsection harmonic_division_v2 (end)
+
+\subsection{Menelaus} % (fold)
+\label{sub:menelaus}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A  = point: new (0 , 0)
+   z.B  = point: new (6 , 0)
+   z.C  = point: new (5 , 4)
+   z.P  = point: new (-1 , 0)
+   z.X  = point: new (6 , 3)
+   L.AC = line: new (z.A,z.C)
+   L.PX = line: new (z.P,z.X)
+   L.BC = line: new (z.B,z.C)
+   z.Q  = intersection (L.AC,L.PX)
+   z.R  = intersection (L.BC,L.PX)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawLine[new](P,R)
+   \tkzDrawLines(P,B A,C B,C)
+   \tkzDrawPoints(P,Q,R,A,B,C)
+   \tkzLabelPoints(A,B,C,P,Q,R)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A   = point: new (0 , 0)
+z.B   = point: new (6 , 0)
+z.C   = point: new (5 , 4)
+z.P   = point: new (-1 , 0)
+z.X   = point: new (6 , 3)
+L.AC  = line: new (z.A,z.C)
+L.PX  = line: new (z.P,z.X)
+L.BC  = line: new (z.B,z.C)
+z.Q   = intersection (L.AC,L.PX)
+z.R   = intersection (L.BC,L.PX)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawLine[new](P,R)
+\tkzDrawLines(P,B A,C B,C)
+\tkzDrawPoints(P,Q,R,A,B,C)
+\tkzLabelPoints(A,B,C,P,Q,R)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Menelaus}
+% subsection menelaus (end)
+
+\subsection{Radical axis v1} % (fold)
+\label{sub:radical_axis_v1}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale   = .75
+   z.X = point : new (0,0)
+   z.B = point : new (2,2)
+   z.Y = point : new (7,1)
+   z.Ap    = point : new (8,-1)
+   L.XY    = line :    new (z.X,z.Y)
+   C.XB    = circle : new (z.X,z.B)
+   C.YAp   = circle : new (z.Y,z.Ap)
+   z.E,z.F = get_points (C.XB : radical_axis (C.YAp))
+   z.A = C.XB : point (-math.pi)
+   T.ABAp  = triangle: new (z.A,z.B,z.Ap)
+   z.O = T.ABAp.circumcenter
+   C.OAp   = circle : new (z.O,z.Ap)
+   _,z.Bp  = intersection (C.OAp,C.YAp)
+   L.AB    = line : new (z.A,z.B)
+   L.ApBp  = line : new (z.Ap,z.Bp)
+   z.M = intersection (L.AB,L.ApBp)
+   z.H = L.XY : projection (z.M)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(X,B Y,A')
+   \tkzDrawArc[dashed,delta=30](O,A')(A)
+   \tkzDrawPoints(A,B,A',B',M,H,X,Y,O,E,F)
+   \tkzDrawLines[red](A,M A',M X,Y E,F)
+   \tkzDrawLines[red,add=1 and 3](M,H)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale    = .75
+z.X      = point : new (0,0)
+z.B      = point : new (2,2)
+z.Y      = point : new (7,1)
+z.Ap     = point : new (8,-1)
+L.XY     = line :    new (z.X,z.Y)
+C.XB     = circle : new (z.X,z.B)
+C.YAp    = circle : new (z.Y,z.Ap)
+z.E,z.F  = get_points (C.XB : radical_axis (C.YAp))
+z.A      = C.XB : point (-math.pi)
+T.ABAp   = triangle: new (z.A,z.B,z.Ap)
+z.O      = T.ABAp.circumcenter
+C.OAp    = circle : new (z.O,z.Ap)
+_,z.Bp   = intersection (C.OAp,C.YAp)
+L.AB     = line : new (z.A,z.B)
+L.ApBp   = line : new (z.Ap,z.Bp)
+z.M      = intersection (L.AB,L.ApBp)
+z.H      = L.XY : projection (z.M)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(X,B Y,A')
+\tkzDrawArc[dashed,delta=30](O,A')(A)
+\tkzDrawPoints(A,B,A',B',M,H,X,Y,O,E,F)
+\tkzDrawLines[red](A,M A',M X,Y E,F)
+\tkzDrawLines[red,add=1 and 3](M,H)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Radical axis v1}
+% subsection radical_axis_v1 (end)
+
+\subsection{Radical axis v2} % (fold)
+\label{sub:radical_axis_v2}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O         = point : new (-1,0)
+   z.Op        = point : new (4,-1)
+   z.B         = point : new (0,2)
+   z.D         = point : new (4,0)
+   C.OB        = circle :    new (z.O,z.B)
+   C.OpD       = circle :    new (z.Op,z.D)
+   L.EF        = C.OB : radical_axis (C.OpD)
+   z.E,z.F     = get_points (L.EF)   
+   z.M         = L.EF : point (2)
+   L.MT,L.MTp  = C.OB : tangent_from (z.M)
+   _,z.T       = get_points (L.MT)
+   _,z.Tp      = get_points (L.MTp)
+   L.MK,L.MKp  = C.OpD : tangent_from (z.M)
+   _,z.K       = get_points (L.MK)
+   _,z.Kp      = get_points (L.MKp)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O,B O',D)
+   \tkzDrawLine[add=1 and 2](E,F)
+   \tkzDrawLine[add=.5 and .5](O,O')
+   \tkzDrawSegments(M,T M,T' M,K M,K')
+   \tkzDrawCircle(M,T)
+   \tkzDrawPoints(O,O',T,M,T',K,K')
+   \tkzLabelPoints(O,O',T,T',K,K',M)
+   \end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale =1.25
+z.O     = point : new (-1,0)
+z.Op    = point : new (4,-1)
+z.B     = point : new (0,2)
+z.D     = point : new (4,0)
+C.OB    = circle :    new (z.O,z.B)
+C.OpD   = circle :    new (z.Op,z.D)
+L.EF    = C.OB : radical_axis (C.OpD)
+z.E,z.F = get_points (L.EF)
+z.M     = L.EF : point (2)
+L.MT,L.MTp  = C.OB : tangent_from (z.M)
+_,z.T = get_points (L.MT)
+_,z.Tp = get_points (L.MTp)
+L.MK,L.MKp  = C.OpD : tangent_from (z.M)
+_,z.K = get_points (L.MK)
+_,z.Kp = get_points (L.MKp)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O,B O',D)
+\tkzDrawLine[add=1 and 2](E,F)
+\tkzDrawLine[add=.5 and .5](O,O')
+\tkzDrawSegments(M,T M,T' M,K M,K')
+\tkzDrawCircle(M,T)
+\tkzDrawPoints(O,O',T,M,T',K,K')
+\tkzLabelPoints(O,O',T,T',K,K',M)
+\end{tikzpicture}\hspace*{\fill}
+%\caption{Radical axis v2}
+% subsection radical_axis_v2 (end)
+
+\subsection{Radical axis v3} % (fold)
+\label{sub:radical_axis_v3}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O     = point : new (0,0)
+   z.B     = point : new (4,0)
+   z.Op    = point : new (6,0)
+   C.OB    = circle :    new (z.O,z.B)
+   C.OpB   = circle :    new (z.Op,z.B)
+   L.EF    = C.OB : radical_axis (C.OpB)
+   z.E,z.F = get_points(L.EF)
+   z.M     = L.EF : point (2)
+   _,L     = C.OB : tangent_from (z.M)
+   _,z.T   = get_points (L)
+   L,_     = C.OpB : tangent_from (z.M)
+   _,z.Tp  = get_points (L)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O,B O',B)
+   \tkzDrawSegments(M,T M,T')
+   \tkzDrawLine[add=.5 and 1](E,F)
+   \tkzDrawLine[add=.5 and .5](O,O')
+   \tkzDrawPoints(O,B,O',E,F,M,T,T')
+   \tkzLabelPoints(O,O',B,E,F,T,T')
+   \tkzDrawArc(M,T')(T)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.O     = point : new (0,0)
+z.B     = point : new (4,0)
+z.Op    = point : new (6,0)
+C.OB    = circle :    new (z.O,z.B)
+C.OpB   = circle :    new (z.Op,z.B)
+L.EF    = C.OB : radical_axis (C.OpB)
+z.E,z.F = get_points(L.EF)
+z.M     = L.EF : point (2)
+_,L     = C.OB : tangent_from (z.M)
+_,z.T   = get_points (L)
+L,_     = C.OpB : tangent_from (z.M)
+_,z.Tp  = get_points (L)
+\end{tkzelements}
+
+
+\hspace*{\fill}  
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O,B O',B)
+\tkzDrawSegments(M,T M,T')
+\tkzDrawLine[add=.5 and 1](E,F)
+\tkzDrawLine[add=.5 and .5](O,O')
+\tkzDrawPoints(O,B,O',E,F,M,T,T')
+\tkzLabelPoints(O,O',B,E,F,T,T')
+\tkzDrawArc(M,T')(T)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Radical axis v3}
+% subsection radical_axis_v3 (end)
+
+\subsection{Radical axis v4} % (fold)
+\label{sub:radical_axis_v4}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O     = point : new (0,0)
+   z.B     = point : new (5,0)
+   z.Op    = point : new (3,0)
+   C.OB    = circle :    new (z.O,z.B)
+   C.OpB   = circle :    new (z.Op,z.B)
+   L.EF    = C.OB : radical_axis (C.OpB)
+   z.E,z.F = get_points(L.EF)
+   z.M     = L.EF : point (1.5)
+   L,_     = C.OB : tangent_from (z.M)
+   _,z.T   = get_points (L)
+   L,_     = C.OpB : tangent_from (z.M)
+   _,z.Tp  = get_points (L)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O,B O',B)
+   \tkzDrawSegments(M,T M,T')
+   \tkzDrawLine[add=1 and 1](E,F)
+   \tkzDrawLine[add=.3 and .3](O,O')
+   \tkzDrawPoints(O,O',B,E,F,T,T',M)
+   \tkzLabelPoints[below right](O,O',B,E,F,T,T')
+   \tkzDrawArc(M,T)(B)
+\end{tikzpicture}
+\end{tkzexample}
+
+
+\begin{tkzelements}
+   z.O     = point : new (0,0)
+   z.B     = point : new (5,0)
+   z.Op    = point : new (3,0)
+   C.OB    = circle :    new (z.O,z.B)
+   C.OpB   = circle :    new (z.Op,z.B)
+   L.EF    = C.OB : radical_axis (C.OpB)
+   z.E,z.F = get_points(L.EF)
+   z.M     = L.EF : point (1.5)
+   L,_     = C.OB : tangent_from (z.M)
+   _,z.T   = get_points (L)
+   L,_     = C.OpB : tangent_from (z.M)
+   _,z.Tp  = get_points (L)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O,B O',B)
+\tkzDrawSegments(M,T M,T')
+\tkzDrawLine[add=1 and 1](E,F)
+\tkzDrawLine[add=.3 and .3](O,O')
+\tkzDrawPoints(O,O',B,E,F,T,T',M)
+\tkzLabelPoints[below right](O,O',B,E,F,T,T')
+\tkzDrawArc(M,T)(B)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Radical axis v4}
+% subsection radical_axis_v4 (end)
+
+\subsection{Radical center} % (fold)
+\label{sub:radical_center}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O      = point : new (0,0)
+   z.x      = point : new (1,0)
+   z.y      = point : new (4,0)
+   z.z      = point : new (2,0)
+   z.Op     = point : new (4,2)
+   z.P      = point : new (2,2.5)
+   C.Ox     = circle :    new (z.O,z.x)
+   C.Pz     = circle :    new (z.P,z.z)
+   C.Opy    = circle :    new (z.Op,z.y)
+   z.ap,z.a = intersection (C.Ox,C.Pz)
+   z.bp,z.b = intersection (C.Opy,C.Pz)
+   L.aap    = line : new (z.a,z.ap)
+   L.bbp    = line : new (z.b,z.bp)
+   z.X      = intersection (L.aap,L.bbp)
+   L.OOp    = line : new (z.O,z.Op)
+   z.H      = L.OOp : projection (z.X)
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O,a O',b P,z)
+   \tkzDrawLines[red](a,X b',X H,X O,O')
+   \tkzDrawPoints(O,O',P,a,a',b,b',X,H)
+   \tkzLabelPoints[below right](O,O',P,H)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.O         = point : new (0,0)
+z.x         = point : new (1,0)
+z.y         = point : new (4,0)
+z.z         = point : new (2,0)
+z.Op        = point : new (4,2)
+z.P         = point : new (2,2.5)
+C.Ox        = circle :    new (z.O,z.x)
+C.Pz        = circle :    new (z.P,z.z)
+C.Opy       = circle :    new (z.Op,z.y)
+z.ap,z.a    = intersection (C.Ox,C.Pz)
+z.bp,z.b    = intersection (C.Opy,C.Pz)
+L.aap       = line : new (z.a,z.ap)
+L.bbp       = line : new (z.b,z.bp)
+z.X         = intersection (L.aap,L.bbp)
+L.OOp       = line : new (z.O,z.Op)
+z.H         = L.OOp : projection (z.X)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O,a O',b P,z)
+\tkzDrawLines[red](a,X b',X H,X O,O')
+\tkzDrawPoints(O,O',P,a,a',b,b',X,H)
+\tkzLabelPoints[below right](O,O',P,H)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Radical center}
+% subsection radical_center (end)
+ 
+\subsection{Hexagram} % (fold)
+\label{sub:hexagram}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A               = point: new (0 , 0)
+   z.B               = point: new (5 , 1)
+   L.AB              = line : new (z.A,z.B)
+   z.C               = point: new (.8 , 3)
+   T.ABC             = triangle: new (z.A,z.B,z.C)
+   z.N               = T.ABC.eulercenter
+   z.G               = T.ABC.centroid
+   z.O               = T.ABC.circumcenter
+   z.H               = T.ABC.orthocenter
+   z.Ma,z.Mb,z.Mc    = get_points (T.ABC : medial ())
+   z.Ha,z.Hb,z.Hc    = get_points (T.ABC : orthic ())   
+   z.Ea,z.Eb,z.Ec    = get_points (T.ABC: extouch())
+   L.euler           = T.ABC : euler_line () 
+   C.circum          = T.ABC : circum_circle () 
+   C.euler           = T.ABC : euler_circle () 
+   z.I,z.J           = intersection (L.euler,C.euler) 
+   E                 = ellipse: foci (z.H,z.O,z.I)  
+   a                 = E.Rx
+   b                 = E.Ry
+   ang               = math.deg(E.slope)
+   L.AH              = line: new (z.A,z.H)
+   L.BH              = line: new (z.B,z.H)
+   L.CH              = line: new (z.C,z.H)
+   z.X               = intersection (L.AH,C.circum)  
+   _,z.Y             = intersection (L.BH,C.circum)  
+   _,z.Z             = intersection (L.CH,C.circum)  
+   L.BC              = line: new (z.B,z.C) 
+   L.XO              = line: new (z.X,z.O)
+   L.YO              = line: new (z.Y,z.O)
+   L.ZO              = line: new (z.Z,z.O)
+   z.x               = intersection (L.BC,L.XO)
+   z.U               = intersection (L.XO,E)
+  _,z.V              = intersection (L.YO,E)
+  _,z.W              = intersection (L.ZO,E)
+   set_lua_to_tex {'a','b','ang'} 
+ \end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircles[red](N,Ma O,A)
+   \tkzDrawSegments(A,X B,Y C,Z B,Hb C,Hc X,O Y,O Z,O)
+   \tkzDrawPolygon[red](U,V,W)
+   \tkzLabelPoints[red](U,V,W)
+   \tkzLabelPoints(A,B,C,X,Y,Z)
+   \tkzDrawLine[blue](I,J)
+   \tkzLabelPoints[blue,right](O,N,G,H,I,J)
+   \tkzDrawPoints(I,J,U,V,W)
+   \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
+   \tkzDrawEllipse[blue](N,\a,\b,\ang)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 1.5
+E = {}
+z.A      = point: new (0 , 0)
+z.B      = point: new (5 , 1)
+L.AB     = line : new (z.A,z.B)
+z.C      = point: new (.8 , 3)
+T.ABC    = triangle: new (z.A,z.B,z.C)
+z.N = T.ABC.eulercenter
+z.G = T.ABC.centroid
+z.O = T.ABC.circumcenter
+z.H = T.ABC.orthocenter
+z.Ma,z.Mb,z.Mc = get_points (T.ABC : medial ())
+z.Ha,z.Hb,z.Hc = get_points (T.ABC : orthic ())   
+z.Ea,z.Eb,z.Ec   = get_points (T.ABC: extouch())
+L.euler      = T.ABC : euler_line () 
+C.circum     = T.ABC : circum_circle () 
+C.euler      = T.ABC : euler_circle () 
+z.I,z.J      = intersection (L.euler,C.euler) 
+ E = ellipse: foci (z.H,z.O,z.I)  
+a = E.Rx
+b = E.Ry
+ang     = math.deg(E.slope)
+L.AH    = line: new (z.A,z.H)
+L.BH    = line: new (z.B,z.H)
+L.CH    = line: new (z.C,z.H)
+z.X     = intersection (L.AH,C.circum)  
+_,z.Y   = intersection (L.BH,C.circum)  
+_,z.Z   = intersection (L.CH,C.circum)  
+L.BC    = line: new (z.B,z.C) 
+L.XO    = line: new (z.X,z.O)
+L.YO    = line: new (z.Y,z.O)
+L.ZO    = line: new (z.Z,z.O)
+z.x     = intersection (L.BC,L.XO)
+z.U     = intersection (L.XO,E)
+_,z.V   = intersection (L.YO,E)
+_,z.W   = intersection (L.ZO,E)
+set_lua_to_tex {'a','b','ang'} 
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircles[red](N,Ma O,A)
+\tkzDrawSegments(A,X B,Y C,Z B,Hb C,Hc X,O Y,O Z,O)
+\tkzDrawPolygon[red](U,V,W)
+\tkzLabelPoints[red](U,V,W)
+\tkzLabelPoints(A,B,C,X,Y,Z)
+\tkzDrawLine[blue](I,J)
+\tkzLabelPoints[blue,right](O,N,G,H,I,J)
+\tkzDrawPoints(I,J,U,V,W)
+\tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
+\tkzDrawEllipse[blue](N,\a,\b,\ang)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Hexagram Lemoine,Pascal}
+% subsection hexagram (end)
+
+\subsection{Gold Arbelos properties} % (fold)
+\label{sub:gold_arbelos_properties}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point : new(0,0)
+   z.B      = point : new(10,0)
+   z.C      = gold_segment_ (z.A,z.B)
+   L.AB     = line:new (z.A,z.B)
+   z.O_1    = L.AB.mid
+   L.AC     = line:new (z.A,z.C)
+   z.O_2    = L.AC.mid
+   L.CB     = line:new (z.C,z.B)
+   z.O_3    = L.CB.mid
+   C1       = circle:new (z.O_1,z.B)
+   C2       = circle:new (z.O_2,z.C)
+   C3       = circle:new (z.O_3,z.B)
+   z.Q      = C2.north
+   z.P      = C3.north
+   L1       = line:new (z.O_2,z.O_3)
+   z.M_0    = L1:harmonic_ext (z.C)
+   L2       = line:new (z.O_1,z.O_2)
+   z.M_1    = L2:harmonic_int (z.A)
+   L3       = line:new (z.O_1,z.O_3)
+   z.M_2    = L3:harmonic_int (z.B)
+   Lbq      = line:new (z.B,z.Q)
+   Lap      = line:new (z.A,z.P)
+   z.S      = intersection (Lbq,Lap)
+   z.x      = z.C: north ()
+   L        = line : new (z.C,z.x)
+   z.D,_    = intersection (L,C1)
+   L.CD     = line :new (z.C,z.D)
+   z.O_7    = L.CD.mid
+   C.DC     = circle: new (z.D,z.C)
+   z.U,z.V  = intersection (C.DC,C1)
+   L.UV     = line :new (z.U,z.V)
+   z.R ,z.S = L.UV : set_projection (z.O_2,z.O_3)
+   L.O1D    = line : new (z.O_1,z.D)
+   z.W      = intersection (L.UV,L.O1D)
+   z.O      = C.DC : inversion (z.W)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[teal](O_1,B)
+   \tkzDrawSemiCircles[thin,teal](O_2,C O_3,B)
+   \tkzDrawArc[purple,delta=0](D,V)(U)
+   \tkzDrawCircle[new](O_7,C)
+   \tkzDrawSegments[thin,purple](A,D D,B C,R C,S C,D U,V)
+   \tkzDrawSegments[thin,red](O,D A,O O,B)
+   \tkzDrawPoints(A,B,C,D,O_7) %,
+   \tkzDrawPoints(O_1,O_2,O_3,U,V,R,S,W,O)
+   \tkzDrawSegments[cyan](O_3,S O_2,R)
+   \tkzDrawSegments[very thin](A,B)
+   \tkzDrawSegments[cyan,thin](C,U U,D)
+   \tkzMarkRightAngles[size=.2,fill=gray!40,opacity=.4](D,C,A A,D,B
+     D,S,C D,W,V O_3,S,U O_2,R,U)
+   \tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_1
+     C,D,B D,C,R B,C,S A,R,O_2)
+   \tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D
+     D,B,C R,C,A O_3,S,B)
+   \tkzLabelPoints[below](C,O_2,O_3,O_1)
+   \tkzLabelPoints[above](D)
+   \tkzLabelPoints[below](O)
+   \tkzLabelPoints[below left](A)
+   \tkzLabelPoints[above left](R)
+   \tkzLabelPoints[above right](S)
+   \tkzLabelPoints[left](V)
+   \tkzLabelPoints[below right](B,U,W,O_7)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A  = point : new(0,0)
+z.B  = point : new(10,0)
+z.C  = gold_segment_ (z.A,z.B)
+L.AB = line:new (z.A,z.B)
+z.O_1    = L.AB.mid
+L.AC = line:new (z.A,z.C)
+z.O_2    = L.AC.mid
+L.CB = line:new (z.C,z.B)
+z.O_3    = L.CB.mid
+C1   = circle:new (z.O_1,z.B)
+C2   = circle:new (z.O_2,z.C)
+C3   = circle:new (z.O_3,z.B)
+z.Q  = C2.north
+z.P  = C3.north
+L1   = line:new (z.O_2,z.O_3)
+z.M_0    = L1:harmonic_ext (z.C)
+L2   = line:new (z.O_1,z.O_2)
+z.M_1    = L2:harmonic_int (z.A)
+L3   = line:new (z.O_1,z.O_3)
+z.M_2    = L3:harmonic_int (z.B)
+Lbq  = line:new (z.B,z.Q)
+Lap  = line:new (z.A,z.P)
+z.S  = intersection (Lbq,Lap)
+z.x  = z.C: north ()
+L    = line : new (z.C,z.x)
+z.D,_    = intersection (L,C1)
+L.CD = line :new (z.C,z.D)
+z.O_7    = L.CD.mid
+C.DC = circle: new (z.D,z.C)
+z.V,z.U  = intersection (C.DC,C1)
+L.UV = line :new (z.U,z.V)
+z.R ,z.S = L.UV : set_projection (z.O_2,z.O_3)
+L.O1D    = line : new (z.O_1,z.D)
+z.W  = intersection (L.UV,L.O1D)
+z.O  = C.DC : inversion (z.W)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[teal](O_1,B)
+\tkzDrawSemiCircles[thin,teal](O_2,C O_3,B)
+\tkzDrawArc[purple,delta=0](D,V)(U)
+\tkzDrawCircle[new](O_7,C)
+\tkzDrawSegments[thin,purple](A,D D,B C,R C,S C,D U,V)
+\tkzDrawSegments[thin,red](O,D A,O O,B)
+\tkzDrawPoints(A,B,C,D,O_7) %,
+\tkzDrawPoints(O_1,O_2,O_3,U,V,R,S,W,O)
+\tkzDrawSegments[cyan](O_3,S O_2,R)
+\tkzDrawSegments[very thin](A,B)
+\tkzDrawSegments[cyan,thin](C,U U,D)
+\tkzMarkRightAngles[size=.2,fill=gray!40,opacity=.4](D,C,A A,D,B
+ D,S,C D,W,V O_3,S,U O_2,R,U)
+\tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_1
+ C,D,B D,C,R B,C,S A,R,O_2)
+\tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D
+ D,B,C R,C,A O_3,S,B)
+\tkzLabelPoints[below](C,O_2,O_3,O_1)
+\tkzLabelPoints[above](D)
+\tkzLabelPoints[below](O)
+\tkzLabelPoints[below left](A)
+\tkzLabelPoints[above left](R)
+\tkzLabelPoints[above right](S)
+\tkzLabelPoints[left](V)
+\tkzLabelPoints[below right](B,U,W,O_7)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Gold Arbelos properties}
+% subsection gold_arbelos_properties (end)
+
+\subsection{Apollonius circle v1 with inversion} % (fold)
+\label{sub:apollonius_circle_v1_with_inversion}
+\begin{tkzexample}[code only,small]
+\begin{tkzelements}
+scale = .75
+  z.A                = point: new (0,0)
+  z.B                = point: new (6,0)
+  z.C                = point: new (0.8,4)
+  T.ABC              = triangle : new (z.A,z.B,z.C) 
+  C.euler            = T.ABC: euler_circle ()
+  z.N,z.Ma           = get_points (C.euler)  
+  z.I_a,z.I_b,z.I_c  = get_points (T.ABC : excentral())
+  z.Ea,z.Eb,z.Ec     = get_points (T.ABC : feuerbach ())
+  -- The Feuerbach triangle is the triangle formed by the three points
+  -- of tangency of the nine-point circle with the excircles
+  z.S,z.p            = get_points (T.ABC: spieker_circle ())
+ --  z.Xa,z.Xb,z.Xc  = get_points (T.ABC : extouch())
+  C.exa              = T.ABC : ex_circle ()
+  z.Ia,z.Xa          = get_points (C.exa)
+  C.exb              = T.ABC : ex_circle (1)
+  z.Ib,z.Xb          = get_points (C.exb)
+  C.exc              = T.ABC : ex_circle (2)
+  z.Ic,z.Xc          = get_points (C.exc)
+  -- S spieker point is the radical center of the last three circles
+  L.fa               = line : new (z.S,z.Ea) 
+  L.fb               = line : new (z.S,z.Eb)
+  L.fc               = line : new (z.S,z.Ec)
+  z.f_a              = intersection (L.fa,C.exa)
+  z.f_b              = intersection (L.fb,C.exb)
+  _,z.f_c            = intersection (L.fc,C.exc)
+  T                  = triangle : new ( z.f_a, z.f_b , z.f_c )
+  z.o                = T.circumcenter
+  _,z.l              = get_points (C.exa : orthogonal_from (z.S))
+  -- S center of inversion !!
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles[red](o,f_a  N,Ma)
+   \tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
+   \tkzClipCircle(o,f_a)
+   \tkzDrawLines[add=3 and 3](A,B A,C B,C)
+   \tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
+   \tkzDrawCircles[cyan](S,l)
+   \tkzDrawPoints(A,B,C)
+   \tkzDrawPoints[cyan](S)
+   \tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
+   \tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.A      = point: new (0,0)
+z.B      = point: new (6,0)
+z.C      = point: new (0.8,4)
+T.ABC    = triangle : new (z.A,z.B,z.C) 
+C.euler      = T.ABC: euler_circle ()
+z.N,z.Ma     = get_points (C.euler)  
+z.I_a,z.I_b,z.I_c    = get_points (T.ABC : excentral())
+z.Ea,z.Eb,z.Ec   = get_points (T.ABC : feuerbach ())
+-- The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles
+z.S,z.p      = get_points (T.ABC: spieker_circle ())
+ --  z.Xa,z.Xb,z.Xc    = get_points (T.ABC : extouch())
+C.exa  = T.ABC : ex_circle ()
+z.Ia,z.Xa  = get_points (C.exa)
+C.exb  = T.ABC : ex_circle (1)
+z.Ib,z.Xb  = get_points (C.exb)
+C.exc  = T.ABC : ex_circle (2)
+z.Ic,z.Xc  = get_points (C.exc)
+
+-- S spieker point is the radical center of the last three circles
+L.fa     = line : new (z.S,z.Ea) 
+L.fb     = line : new (z.S,z.Eb)
+L.fc     = line : new (z.S,z.Ec)
+z.f_a    = intersection (L.fa,C.exa)
+z.f_b    = intersection (L.fb,C.exb)
+_,z.f_c      = intersection (L.fc,C.exc)
+T  = triangle : new ( z.f_a, z.f_b , z.f_c )
+z.o      = T.circumcenter
+_,z.l    = get_points (C.exa : orthogonal_from (z.S))
+-- S center of inversion !!
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[red](o,f_a  N,Ma)
+\tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
+\tkzClipCircle(o,f_a)
+\tkzDrawLines[add=3 and 3](A,B A,C B,C)
+\tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
+\tkzDrawCircles[cyan](S,l)
+\tkzDrawPoints(A,B,C)
+\tkzDrawPoints[cyan](S)
+\tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
+\tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Apollonius circle V1}
+% subsection apollonius_circle_v1_with_inversion (end)
+
+\subsection{Apollonius circle v2} % (fold)
+\label{sub:apollonius_circle_v2}
+ \begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   scale       = .5
+   z.A         = point: new (0,0)
+   z.B         = point: new (6,0)
+   z.C         = point: new (0.8,4)
+   T.ABC       = triangle: new(z.A,z.B,z.C)
+   z.O         = T.ABC.circumcenter
+   z.H         = T.ABC.orthocenter
+   z.G         = T.ABC.centroid
+   z.L         = T.ABC: lemoine_point ()
+   z.S         = T.ABC: spieker_center ()
+   C.euler     = T.ABC: euler_circle ()
+   z.N,z.Ma    = get_points (C.euler) 
+   C.exA       = T.ABC : ex_circle ()
+   z.Ja,z.Xa   = get_points (C.exA)
+   C.exB       = T.ABC : ex_circle (1)
+   z.Jb,z.Xb   = get_points (C.exB)
+   C.exC       = T.ABC : ex_circle (2)
+   z.Jc,z.Xc   = get_points (C.exC)
+   L.OL        = line: new (z.O,z.L)
+   L.NS        = line: new (z.N,z.S)
+   z.o         = intersection (L.OL,L.NS) -- center of Apollonius circle
+   L.NMa       = line: new (z.N,z.Ma)
+   L.ox        = L.NMa: ll_from (z.o)
+   L.MaS       = line: new (z.Ma,z.S)
+   z.t         = intersection (L.ox,L.MaS) -- through
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[add=1 and 1](A,B A,C B,C) 
+   \tkzDrawCircles(Ja,Xa Jb,Xb Jc,Xc o,t N,Ma) %
+   \tkzClipCircle(o,t)
+   \tkzDrawLines[red](o,L N,o Ma,t)
+   \tkzDrawLines[cyan,add=4 and 4](Ma,N o,t)
+   \tkzDrawPoints(A,B,C,Ma,Ja,Jb,Jc)
+   \tkzDrawPoints[red](N,O,L,S,o,t)
+   \tkzLabelPoints[right,font=\tiny](A,B,C,Ja,Jb,Jc,O,N,L,S,Ma,o)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale =.5
+z.A    = point: new (0,0)
+z.B    = point: new (6,0)
+z.C    = point: new (0.8,4)
+T.ABC  = triangle: new(z.A,z.B,z.C)
+z.O    = T.ABC.circumcenter
+z.H    = T.ABC.orthocenter
+z.G    = T.ABC.centroid
+z.L    = T.ABC: lemoine_point ()
+z.S    = T.ABC: spieker_center ()
+C.euler    = T.ABC: euler_circle ()
+z.N,z.Ma   = get_points (C.euler) 
+C.exA  = T.ABC : ex_circle ()
+z.Ja,z.Xa  = get_points (C.exA)
+C.exB  = T.ABC : ex_circle (1)
+z.Jb,z.Xb  = get_points (C.exB)
+C.exC  = T.ABC : ex_circle (2)
+z.Jc,z.Xc  = get_points (C.exC)
+L.OL   = line: new (z.O,z.L)
+L.NS   = line: new (z.N,z.S)
+z.o    = intersection (L.OL,L.NS) -- center of Apollonius circle
+L.NMa  = line: new (z.N,z.Ma)
+L.ox   = L.NMa: ll_from (z.o)
+L.MaS  = line: new (z.Ma,z.S)
+z.t    = intersection (L.ox,L.MaS) -- through
+\end{tkzelements}
+
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines[add=1 and 1](A,B A,C B,C) 
+\tkzDrawCircles(Ja,Xa Jb,Xb Jc,Xc o,t N,Ma) %
+\tkzClipCircle(o,t)
+\tkzDrawLines[red](o,L N,o Ma,t)
+\tkzDrawLines[cyan,add=4 and 4](Ma,N o,t)
+\tkzDrawPoints(A,B,C,Ma,Ja,Jb,Jc)
+\tkzDrawPoints[red](N,O,L,S,o,t)
+\tkzLabelPoints[right,font=\tiny](A,B,C,Ja,Jb,Jc,O,N,L,S,Ma,o)
+\end{tikzpicture}
+\hspace*{\fill}
+% subsection apollonius_circle_v2 (end)
+
+
+\subsection{Orthogonal circles v1} % (fold)
+\label{sub:orthogonal_circles_v1}
+
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   scale    = .6
+   z.C_1    = point: new (0,0)
+   z.C_2    = point: new (8,0)
+   z.A      = point: new (5,0)
+   C        = circle: new (z.C_1,z.A)
+   z.S,z.T  = get_points (C: orthogonal_from (z.C_2))
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(C_1,T C_2,T)
+   \tkzDrawSegments(C_1,T C_2,T)
+   \tkzDrawLine(C_1,C_2)
+   \tkzMarkRightAngle[fill=teal,%
+  opacity=.2,size=1](C_1,T,C_2)
+   \tkzDrawPoints(C_1,C_2,T)
+   \tkzLabelPoints(C_1,C_2)
+   \tkzLabelPoints[above](T)
+   \tkzLabelSegment[left](C_1,T){r}
+   \tkzLabelSegments[right](C_2,T){\gamma}
+   \tkzLabelSegment[below](C_1,C_2){d}
+   \tkzLabelCircle[left=10pt](C_1,T)(180){Circle 1}
+   \tkzLabelCircle[right=10pt](C_2,T)(180){Circle 2}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale    = .6
+z.C_1    = point: new (0,0)
+z.C_2    = point: new (8,0)
+z.A  = point: new (5,0)
+C    = circle: new (z.C_1,z.A)
+z.S,z.T  = get_points (C: orthogonal_from (z.C_2))
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(C_1,T C_2,T)
+\tkzDrawSegments(C_1,T C_2,T)
+\tkzDrawLine(C_1,C_2)
+\tkzMarkRightAngle[fill=teal,opacity=.2,size=.5](C_1,T,C_2)
+\tkzDrawPoints(C_1,C_2,T)
+\tkzLabelPoints(C_1,C_2)
+\tkzLabelPoints[above](T)
+\tkzLabelSegment[left](C_1,T){r}
+\tkzLabelSegments[right](C_2,T){\gamma}
+\tkzLabelSegment[below](C_1,C_2){d}
+\tkzLabelCircle[left=10pt](C_1,T)(180){Circle 1}
+\tkzLabelCircle[right=10pt](C_2,T)(180){Circle 2}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Orthogonal circles v1 }
+% subsection orthogonal_circles_v1 (end)
+
+\subsection{Orthogonal circles v2} % (fold)
+\label{sub:orthogonal_circles_v2}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale       = .75
+   z.O         = point: new (2,2)
+   z.Op        = point: new (-4,1)
+   z.P         = point: polar (4,0)
+   C.OP        = circle: new (z.O,z.P)
+   C.Oz1,C.Oz2 = C.OP : orthogonal_from (z.Op)
+   z.z1        = C.Oz1.through
+   z.z2        = C.Oz2.through
+   L.OP        = line : new (z.O,z.P)
+   C.Opz1      = circle: new (z.Op,z.z1)
+   L.T,L.Tp    = C.Opz1 : tangent_from (z.O)
+   z.T         = L.T.pb
+   z.Tp        = L.Tp.pb
+   L.OOp       = line : new (z.O,z.Op)
+   z.M         = L.OOp.mid
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes  
+   \tkzDrawCircle[red](O,P)
+   \tkzDrawCircle[purple](O',z1)
+   \tkzDrawCircle[cyan](M,T)
+   \tkzDrawSegments(O',T O,T' O',T')
+   \tkzDrawSegment[purple](O',T)
+   \tkzDrawSegments[red](O,T O,O')
+   \tkzDrawPoints(O,O',T,T',M)
+   \tkzMarkRightAngle[fill=gray!10](O',T,O)
+   \tkzLabelPoint[below](O){$O$}
+   \tkzLabelPoint[above](T){$T$}
+   \tkzLabelPoint[above](M){$M$}
+   \tkzLabelPoint[below](T'){$T'$}
+   \tkzLabelPoint[above left](O'){$O'$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .75
+z.O     = point: new (2,2)
+z.Op    = point: new (-4,1)
+z.P     = point: polar (4,0)
+C.OP    = circle: new (z.O,z.P)
+C.Oz1,C.Oz2 =  C.OP : orthogonal_from (z.Op)
+z.z1  = C.Oz1.through
+z.z2  = C.Oz2.through
+L.OP    = line : new (z.O,z.P)
+C.Opz1  = circle: new (z.Op,z.z1)
+L.T,L.Tp   = C.Opz1 : tangent_from (z.O)
+z.T   = L.T.pb
+z.Tp   = L.Tp.pb
+L.OOp   = line : new (z.O,z.Op)
+z.M     = L.OOp.mid
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes  
+\tkzDrawCircle[red](O,P)
+\tkzDrawCircle[purple](O',z1)
+\tkzDrawCircle[cyan](M,T)
+\tkzDrawSegments(O',T O,T' O',T')
+\tkzDrawSegment[purple](O',T)
+\tkzDrawSegments[red](O,T O,O')
+\tkzDrawPoints(O,O',T,T',M)
+\tkzMarkRightAngle[fill=gray!10](O',T,O)
+\tkzLabelPoint[below](O){$O$}
+\tkzLabelPoint[above](T){$T$}
+\tkzLabelPoint[above](M){$M$}
+\tkzLabelPoint[below](T'){$T'$}
+\tkzLabelPoint[above left](O'){$O'$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Orthogonal circles v2}
+% subsection orthogonal_circles_v2 (end)
+
+\subsection{Orthogonal circle to two circles} % (fold)
+\label{sub:orthogonal_circle_to_two_circles}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O         = point :   new (-1,0)
+   z.B         = point :   new (0,2)
+   z.Op        = point :   new (4,-1)
+   z.D         = point :   new (4,0)
+   C.OB        = circle :  new (z.O,z.B)
+   C.OpD       = circle :  new (z.Op,z.D)
+   z.E,z.F     = get_points (C.OB : radical_axis (C.OpD))
+   L.EF        = line : new (z.E,z.F)
+   z.M         = L.EF : point (2.25)
+   L.T,L.Tp    = C.OB : tangent_from (z.M)
+   L.K,L.Kp    = C.OpD : tangent_from (z.M)
+   z.T         = L.T.pb
+   z.K         = L.K.pb
+   z.Tp        = L.Tp.pb
+   z.Kp        = L.Kp.pb
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes   
+   \tkzDrawCircles(O,B O',D)
+   \tkzDrawLine[add=1 and 2,cyan](E,F)
+   \tkzDrawLines[add=.5 and .5,orange](O,O' O,T O,T')
+   \tkzDrawSegments[cyan](M,T M,T' M,K M,K')
+   \tkzDrawCircle(M,T)
+   \tkzDrawPoints(O,O',T,M,T',K,K')
+   \tkzLabelPoints(O,O',T,T',M,K,K')
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.O   = point :   new (-1,0)
+z.B   = point :   new (0,2)
+z.Op  = point :   new (4,-1)
+z.D   = point :   new (4,0)
+C.OB  = circle :  new (z.O,z.B)
+C.OpD = circle :  new (z.Op,z.D)
+z.E,z.F   = get_points (C.OB : radical_axis (C.OpD))
+L.EF  = line : new (z.E,z.F)
+z.M   = L.EF : point (2.25)
+L.T,L.Tp  = C.OB : tangent_from (z.M)
+L.K,L.Kp  = C.OpD : tangent_from (z.M)
+z.T = L.T.pb
+z.K = L.K.pb
+z.Tp = L.Tp.pb
+z.Kp = L.Kp.pb
+\end{tkzelements}
+
+ 
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes   
+\tkzDrawCircles(O,B O',D)
+\tkzDrawLine[add=1 and 2,cyan](E,F)
+\tkzDrawLines[add=.5 and .5,orange](O,O' O,T O,T')
+\tkzDrawSegments[cyan](M,T M,T' M,K M,K')
+\tkzDrawCircle(M,T)
+\tkzDrawPoints(O,O',T,M,T',K,K')
+\tkzLabelPoints(O,O',T,T',M,K,K')
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Orthogonal to two circles}
+% \subsection{Orthogonal to two circles} % (fold)
+
+\subsection{Midcircles} % (fold)
+\label{sub:midcircles}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (10 , 0)
+   L.AB     = line : new (z.A,z.B)
+   z.C      = L.AB: gold_ratio ()
+   L.AC     = line : new (z.A,z.C)
+   L.CB     = line : new (z.C,z.B)
+   z.O_0    = L.AB.mid
+   z.O_1    = L.AC.mid
+   z.O_2    = L.CB.mid
+   C.O0B    = circle : new (z.O_0,z.B)
+   C.O1C    = circle : new (z.O_1,z.C)
+   C.O2C    = circle : new (z.O_2,z.B)
+   z.Q      = C.O1C : midarc (z.C,z.A)
+   z.P      = C.O2C : midarc (z.B,z.C)
+   L.O1O2   = line : new (z.O_1,z.O_2) 
+   L.O0O1   = line : new (z.O_0,z.O_1) 
+   L.O0O2   = line : new (z.O_0,z.O_2)
+   z.M_0    = L.O1O2 : harmonic_ext (z.C)
+   z.M_1    = L.O0O1 : harmonic_int (z.A)
+   z.M_2    = L.O0O2 : harmonic_int (z.B)  
+   L.BQ     = line : new (z.B,z.Q)
+   L.AP     = line : new (z.A,z.P)
+   z.S      = intersection (L.BQ,L.AP)
+   L.CS     = line : new (z.C,z.S)
+   C.M1A    = circle : new (z.M_1,z.A)
+   C.M2B    = circle : new (z.M_2,z.B)
+   z.P_0    = intersection (L.CS,C.O0B)
+   z.P_1    = intersection (C.M2B,C.O1C)
+   z.P_2    = intersection (C.M1A,C.O2C)
+   T.P012   = triangle : new (z.P_0,z.P_1,z.P_2)
+   z.O_4    = T.P012.circumcenter
+   T.CP12   = triangle : new (z.C,z.P_1,z.P_2)
+   z.O_5    = T.CP12.circumcenter
+   z.BN     = z.B : north ()
+   L.BBN    = line : new (z.B,z.BN)
+   L.M1P2   = line : new (z.M_1,z.P_2)
+   z.J      = intersection (L.BBN,L.M1P2)
+   L.AP0    = line : new (z.A,z.P_0)
+   L.BP0    = line : new (z.B,z.P_0)
+   C.O4P0   = circle : new (z.O_4,z.P_0)
+   _,z.G    = intersection (L.AP0,C.O4P0)
+   z.H      = intersection (L.BP0,C.O4P0)
+   z.Ap     = z.M_1: symmetry (z.A)
+   z.H_4,z.F,z.E,z.H_0 = L.AB : set_projection (z.O_4,z.G,z.H,z.P_0)
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle[thin,fill=green!10](O_4,P_0)
+   \tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C)
+   \tkzDrawSemiCircles[teal](O_0,B)
+   \tkzDrawSemiCircles[thin,teal,fill=teal!20,opacity=.5](O_1,C O_2,B)
+   \tkzDrawSemiCircles[new](M_2,B)
+   \tkzDrawSemiCircles[new](M_1,A')
+   \tkzDrawArc[purple,delta=0](M_0,P_0)(C)
+   \tkzDrawSegments[very thin](A,B A,P B,Q)
+   \tkzDrawSegments[step 1](O_0,P_0 B,J G,J G,O_0 H,O_2)
+   \tkzDrawSegments[ultra thin,purple](M_1,P_0 M_2,P_0 M_1,M_0 M_0,P_1 M_0,P_0 M_1,J)
+   \tkzDrawPoints(A,B,C,P_0,P_2,P_1,M_0,M_1,M_2,J,P,Q,S)
+   \tkzDrawPoints(O_0,O_1,O_2,O_4,O_5,G,H)
+   \tkzMarkRightAngle[size=.2,fill=gray!20,opacity=.4](O_0,P_0,M_0)
+   \tkzLabelPoints[below](A,B,C,M_0,M_1,M_2,O_1,O_2,O_0)
+   \tkzLabelPoints[above](P_0,O_5,O_4)
+   \tkzLabelPoints[above](P_1,J)
+   \tkzLabelPoints[above](P_2,P,Q,S)
+   \tkzLabelPoints[above right](H,E)
+   \tkzLabelPoints[above left](F,G)
+   \tkzLabelPoints[below right](H_0)
+   \tkzLabelCircle[below=4pt,font=\scriptsize](O_1,C)(80){$(\beta)$}
+   \tkzLabelCircle[below=4pt,font=\scriptsize](O_2,B)(80){$(\gamma)$}
+   \tkzLabelCircle[below=4pt,font=\scriptsize](O_0,B)(110){$(\alpha)$}
+   \tkzLabelCircle[left,font=\scriptsize](O_4,P_2)(60){$(\delta)$}
+   \tkzLabelCircle[above left,font=\scriptsize](O_5,C)(40){$(\epsilon)$}
+   \end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A  = point: new (0 , 0)
+z.B  = point: new (10 , 0)
+L.AB = line : new (z.A,z.B)
+z.C  = L.AB: gold_ratio ()
+L.AC = line : new (z.A,z.C)
+L.CB = line : new (z.C,z.B)
+z.O_0    = L.AB.mid
+z.O_1    = L.AC.mid
+z.O_2    = L.CB.mid
+C.O0B    = circle : new (z.O_0,z.B)
+C.O1C    = circle : new (z.O_1,z.C)
+C.O2C    = circle : new (z.O_2,z.B)
+z.Q  = C.O1C : midarc (z.C,z.A)
+z.P  = C.O2C : midarc (z.B,z.C)
+L.O1O2   = line : new (z.O_1,z.O_2) 
+L.O0O1   = line : new (z.O_0,z.O_1) 
+L.O0O2   = line : new (z.O_0,z.O_2)
+z.M_0    = L.O1O2 : harmonic_ext (z.C)
+z.M_1    = L.O0O1 : harmonic_int (z.A)
+z.M_2    = L.O0O2 : harmonic_int (z.B)  
+L.BQ = line : new (z.B,z.Q)
+L.AP = line : new (z.A,z.P)
+z.S  = intersection (L.BQ,L.AP)
+L.CS = line : new (z.C,z.S)
+C.M1A    = circle : new (z.M_1,z.A)
+C.M2B    = circle : new (z.M_2,z.B)
+z.P_0    = intersection (L.CS,C.O0B)
+z.P_1    = intersection (C.M2B,C.O1C)
+z.P_2    = intersection (C.M1A,C.O2C)
+T.P012   = triangle : new (z.P_0,z.P_1,z.P_2)
+z.O_4    = T.P012.circumcenter
+T.CP12   = triangle : new (z.C,z.P_1,z.P_2)
+z.O_5    = T.CP12.circumcenter
+z.BN = z.B : north ()
+L.BBN    = line : new (z.B,z.BN)
+L.M1P2   = line : new (z.M_1,z.P_2)
+z.J  = intersection (L.BBN,L.M1P2)
+L.AP0    = line : new (z.A,z.P_0)
+L.BP0    = line : new (z.B,z.P_0)
+C.O4P0   = circle : new (z.O_4,z.P_0)
+_,z.G  = intersection (L.AP0,C.O4P0)
+z.H    = intersection (L.BP0,C.O4P0)
+z.Ap = z.M_1: symmetry (z.A)
+z.H_4,z.F,z.E,z.H_0 = L.AB : set_projection (z.O_4,z.G,z.H,z.P_0)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircle[thin,fill=green!10](O_4,P_0)
+\tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C)
+\tkzDrawSemiCircles[teal](O_0,B)
+\tkzDrawSemiCircles[thin,teal,fill=teal!20,opacity=.5](O_1,C O_2,B)
+\tkzDrawSemiCircles[color = orange](M_2,B)
+\tkzDrawSemiCircles[color = orange](M_1,A')
+\tkzDrawArc[purple,delta=0](M_0,P_0)(C)
+\tkzDrawSegments[very thin](A,B A,P B,Q)
+\tkzDrawSegments[color=cyan](O_0,P_0 B,J G,J G,O_0 H,O_2)
+\tkzDrawSegments[ultra thin,purple](M_1,P_0 M_2,P_0 M_1,M_0 M_0,P_1 M_0,P_0 M_1,J)
+\tkzDrawPoints(A,B,C,P_0,P_2,P_1,M_0,M_1,M_2,J,P,Q,S)
+\tkzDrawPoints(O_0,O_1,O_2,O_4,O_5,G,H)
+\tkzMarkRightAngle[size=.2,fill=gray!20,opacity=.4](O_0,P_0,M_0)
+\tkzLabelPoints[below](A,B,C,M_0,M_1,M_2,O_1,O_2,O_0)
+\tkzLabelPoints[above](P_0,O_5,O_4)
+\tkzLabelPoints[above](P_1,J)
+\tkzLabelPoints[above](P_2,P,Q,S)
+\tkzLabelPoints[above right](H,E)
+\tkzLabelPoints[above left](F,G)
+\tkzLabelPoints[below right](H_0)
+\tkzLabelCircle[below=4pt,font=\scriptsize](O_1,C)(80){$(\beta)$}
+\tkzLabelCircle[below=4pt,font=\scriptsize](O_2,B)(80){$(\gamma)$}
+\tkzLabelCircle[below=4pt,font=\scriptsize](O_0,B)(110){$(\alpha)$}
+\tkzLabelCircle[left,font=\scriptsize](O_4,P_2)(60){$(\delta)$}
+\tkzLabelCircle[above left,font=\scriptsize](O_5,C)(40){$(\epsilon)$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Midcircles}
+% subsection midcircles (end)
+
+\subsection{Pencil v1} % (fold)
+\label{sub:pencil_v1}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale       = .75
+   z.A         = point : new (0,2)
+   z.B         = point : new (0,-2)
+   z.C_0       = point : new (-3,0)
+   z.C_1       = point : new (2,0)
+   z.C_3       = point : new (2.5,0)
+   z.C_5       = point : new (1,0)
+   L.BA        = line : new (z.B,z.A)
+   z.M_0       = L.BA : point (1.25)
+   z.M_1       = L.BA : point (1.5)
+   C.C0A       = circle :    new (z.C_0,z.A)
+   z.x,z.y     = get_points (C.C0A : orthogonal_from (z.M_0))
+   z.xp,z.yp   = get_points (C.C0A : orthogonal_from (z.M_1))
+   z.O         = L.BA.mid
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(C_0,A C_1,A C_3,A C_5,A)
+   \tkzDrawCircles[thick,color=red](M_0,x M_1,x')
+   \tkzDrawCircles[thick,color=blue](O,A)
+   \tkzDrawLines(C_0,C_1 B,M_1)
+   \tkzDrawPoints(A,B,C_0,C_1,M_0,M_1,x,y)
+   \tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,x,y)
+   \tkzLabelLine[pos=1.25,right]( M_0,M_1){$(\Delta)$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale=.75
+z.A     = point : new (0,2)
+z.B     = point : new (0,-2)
+z.C_0   = point : new (-3,0)
+z.C_1   = point : new (2,0)
+z.C_3   = point : new (2.5,0)
+z.C_5   = point : new (1,0)
+L.BA    = line : new (z.B,z.A)
+z.M_0   = L.BA : point (1.25)
+z.M_1   = L.BA : point (1.5)
+C.C0A   = circle :    new (z.C_0,z.A)
+z.x,z.y = get_points (C.C0A : orthogonal_from (z.M_0))
+z.xp,z.yp   = get_points (C.C0A : orthogonal_from (z.M_1))
+z.O     = L.BA.mid
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(C_0,A C_1,A C_3,A C_5,A)
+\tkzDrawCircles[thick,color=red](M_0,x M_1,x')
+\tkzDrawCircles[thick,color=blue](O,A)
+\tkzDrawLines(C_0,C_1 B,M_1)
+\tkzDrawPoints(A,B,C_0,C_1,M_0,M_1,x,y)
+\tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,x,y)
+\tkzLabelLine[pos=1.25,right]( M_0,M_1){$(\Delta)$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Pencil v1}
+% subsection pencil_v1 (end)
+
+\subsection{Pencil v2} % (fold)
+\label{sub:pencil_v2}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale=.75
+   z.A     = point : new (0,0)
+   z.B     = point : new (1,0)
+   z.C_0   = point : new (-2,0)
+   z.C_1   = point : new (4,0)
+   C.C0A   = circle : new (z.C_0,z.A)
+   C.C1B   = circle : new (z.C_1,z.B)
+   L.EF    = C.C0A : radical_axis (C.C1B)
+   z.M_0   = L.EF : point (2)
+   z.M_1   = L.EF : point (-1)
+   z.M_2   = L.EF : point (-2)
+   C.orth0     = C.C0A : orthogonal_from (z.M_0)
+   C.orth1     = C.C0A : orthogonal_from (z.M_1)
+   C.orth2     = C.C0A : orthogonal_from (z.M_2)
+   z.u         = C.orth0.through
+   z.v         = C.orth1.through
+   z.t         = C.orth2.through
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(C_0,A C_1,B)
+   \tkzDrawCircles[thick,color=red](M_0,u M_1,v M_2,t)
+   \tkzDrawLines[add= .75 and .75](C_0,C_1 M_0,M_1)
+   \tkzDrawPoints(A,B,C_0,C_1,M_0,M_1,M_2)
+   \tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,M_2)
+   \tkzLabelLine[pos=2,right]( M_0,M_1){$(\Delta)$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale=.75
+   z.A     = point : new (0,0)
+   z.B     = point : new (1,0)
+   z.C_0   = point : new (-2,0)
+   z.C_1   = point : new (4,0)
+   C.C0A   = circle :    new (z.C_0,z.A)
+   C.C1B   = circle : new (z.C_1,z.B)
+   L.EF    = C.C0A : radical_axis (C.C1B)
+   z.M_0   = L.EF : point (2)
+   z.M_1   = L.EF : point (-1)
+   z.M_2   = L.EF : point (-2)
+   C.orth0     = C.C0A : orthogonal_from (z.M_0)
+   C.orth1     = C.C0A : orthogonal_from (z.M_1)
+   C.orth2     = C.C0A : orthogonal_from (z.M_2)
+   z.u         = C.orth0.through
+   z.v         = C.orth1.through
+   z.t         = C.orth2.through
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(C_0,A C_1,B)
+\tkzDrawCircles[thick,color=red](M_0,u M_1,v M_2,t)
+\tkzDrawLines[add= .75 and .75](C_0,C_1 M_0,M_1)
+\tkzDrawPoints(A,B,C_0,C_1,M_0,M_1,M_2)
+\tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,M_2)
+\tkzLabelLine[pos=2,right]( M_0,M_1){$(\Delta)$}
+\end{tikzpicture}
+\hspace*{\fill}
+%subsection pencil_v2 (end)
+
+\subsection{Power v1} % (fold)
+\label{sub:power_v1}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O     = point : new (0,0)
+   z.A     = point : new (2,-2)
+   z.M     = point : new (-6,0)
+   L.AM    = line : new (z.A,z.M)
+   C.OA    = circle :    new (z.O,z.A)
+   z.Ap    = C.OA : antipode (z.A)
+   z.B     = intersection (L.AM, C.OA)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(O,A)
+   \tkzMarkRightAngle[fill=gray!10](A',B,M)
+   \tkzDrawSegments(M,O A,A' A',B)
+   \tkzDrawPoints(O,A,A',M,B)
+   \tkzLabelPoints(O,A,A',M,B)
+   \tkzDrawSegments[-Triangle](M,A M,A')
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 1.25
+z.O   = point : new (0,0)
+z.A   = point : new (2,-2)
+z.M   = point : new (-6,0)
+L.AM  = line : new (z.A,z.M)
+C.OA  = circle : new (z.O,z.A)
+z.Ap  = C.OA : antipode (z.A)
+z.B   = intersection (L.AM, C.OA)
+\end{tkzelements}
+ 
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircle(O,A)
+\tkzMarkRightAngle[fill=gray!10](A',B,M)
+\tkzDrawSegments(M,O A,A' A',B)
+\tkzDrawPoints(O,A,A',M,B)
+\tkzLabelPoints(O,A,A',M,B)
+\tkzDrawSegments[-Triangle](M,A M,A')
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Power v1}
+% subsection power_v1 (end)
+
+\subsection{Power v2} % (fold)
+\label{sub:power_v2}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O     = point : new (0,0)
+   z.A     = point : new (2,2)
+   z.M     = point : new (-1.5,0)
+   L.AM    = line : new (z.A,z.M)
+   C.OA    = circle :    new (z.O,z.A)
+   z.Ap    = C.OA : antipode (z.A)
+   _,z.B   = intersection (L.AM, C.OA)
+   z.m     = z.M : north(1)
+   L.mM    = line : new (z.m,z.M)
+   z.U,z.V = intersection (L.mM,C.OA)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(O,A)
+   \tkzMarkRightAngle[fill=gray!10](A',B,M)
+   \tkzDrawSegments(M,O A,A' A',B A,B U,V)
+   \tkzDrawPoints(O,A,A',M,B,U,V,m)
+   \tkzLabelPoints(O,A,M,U,V,m)
+   \tkzLabelPoints[below left](A',B)
+   \tkzDrawSegments(M,A M,A')
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 1.25
+z.O     = point : new (0,0)
+z.A     = point : new (2,2)
+z.M     = point : new (-1.5,0)
+L.AM    = line : new (z.A,z.M)
+C.OA    = circle :    new (z.O,z.A)
+z.Ap    = C.OA : antipode (z.A)
+_,z.B   = intersection (L.AM, C.OA)
+z.m     = z.M : north(1)
+L.mM    = line : new (z.m,z.M)
+z.U,z.V = intersection (L.mM,C.OA)
+\end{tkzelements}
+
+\hspace*{\fill}\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircle(O,A)
+\tkzMarkRightAngle[fill=gray!10](A',B,M)
+\tkzDrawSegments(M,O A,A' A',B A,B U,V)
+\tkzDrawPoints(O,A,A',M,B,U,V,m)
+\tkzLabelPoints(O,A,M,U,V,m)
+\tkzLabelPoints[below left](A',B)
+\tkzDrawSegments(M,A M,A')
+\end{tikzpicture}\hspace*{\fill}
+ %\caption{Power v2}
+% subsection power_v2 (end)
+
+\subsection{Reim v1} % (fold)
+\label{sub:reim_v1}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A     = point: new (0,0)
+   z.E     = point: new (-2,2)
+   C.AE    = circle :   new (z.A,z.E)
+   z.C     = C.AE : point (math.pi/6)
+   z.D     = C.AE : point (-math.pi/180*40)
+   z.F     = C.AE : point (-math.pi/180*100)
+   L.EC    = line: new (z.E,z.C)
+   z.H     = L.EC : point (1.5)
+   T.CDH   = triangle : new (z.C,z.D,z.H)
+   z.B     = T.CDH.circumcenter
+   C.BD    = circle : new (z.B,z.D)
+   L.FD    = line: new (z.F,z.D)
+   z.G     = intersection (L.FD,C.BD)
+   z.O     = intersection (L.EC,L.FD)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(A,E B,H)
+   \tkzDrawSegments(E,D C,F)
+   \tkzDrawLines(E,O F,O)
+   \tkzDrawLines[red](E,F H,G)
+   \tkzDrawPoints(A,...,H,O)
+   \tkzLabelPoints(A,B,D,F,G,O)
+   \tkzLabelPoints[above](E,C,H)
+   \tkzMarkAngles[size=.5](E,C,F E,D,F)
+   \tkzFillAngles[green!40,opacity=.4,size=.5](E,C,F E,D,F)
+   \tkzMarkAngles[size=.5](F,C,H G,D,E)
+   \tkzFillAngles[red!40,opacity=.4,size=.5](F,C,H G,D,E)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A     = point: new (0,0)
+z.E     = point: new (-2,2)
+C.AE    = circle :   new (z.A,z.E)
+z.C     = C.AE : point (math.pi/6)
+z.D     = C.AE : point (-math.pi/180*40)
+z.F     = C.AE : point (-math.pi/180*100)
+L.EC    = line: new (z.E,z.C)
+z.H     = L.EC : point (1.5)
+T.CDH   = triangle : new (z.C,z.D,z.H)
+z.B     = T.CDH.circumcenter
+C.BD    = circle : new (z.B,z.D)
+L.FD    = line: new (z.F,z.D)
+z.G     = intersection (L.FD,C.BD)
+z.O     = intersection (L.EC,L.FD)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(A,E B,H)
+\tkzDrawSegments(E,D C,F)
+\tkzDrawLines(E,O F,O)
+\tkzDrawLines[red](E,F H,G)
+\tkzDrawPoints(A,...,H,O)
+\tkzLabelPoints(A,B,D,F,G,O)
+\tkzLabelPoints[above](E,C,H)
+\tkzMarkAngles[size=.5](E,C,F E,D,F)
+\tkzFillAngles[green!40,opacity=.4,size=.5](E,C,F E,D,F)
+\tkzMarkAngles[size=.5](F,C,H G,D,E)
+\tkzFillAngles[red!40,opacity=.4,size=.5](F,C,H G,D,E)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Reim v1}
+% subsection reim_v1 (end)
+
+\subsection{Reim v2} % (fold)
+\label{sub:reim_v2}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale    = .6
+   z.A      = point: new (0,0)
+   z.B      = point: new (10,0)
+   z.C      = point: new (4,0)
+   C.AC     = circle: new (z.A,z.C)
+   z.c,z.cp = get_points (C.AC: tangent_at (z.C))
+   z.M      = C.AC: point (1.2*math.pi)
+   L.MC     = line: new (z.M,z.C)
+   C.BC     = circle: new (z.B,z.C)
+   z.N      = intersection (L.MC,C.BC)
+   z.m,z.mp = get_points (C.AC: tangent_at (z.M))
+   z.n,z.np = get_points (C.BC: tangent_at (z.N))
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(A,C B,C)
+   \tkzDrawLines[new,add=1 and 1](M,m N,n C,c)
+   \tkzDrawSegment(M,N)
+   \tkzDrawPoints(A,B,C,M,N)
+   \tkzLabelPoints[below right](A,B,C,M,N)
+   \tkzFillAngles[blue!30,opacity=.3](m',M,C N,C,c' M,C,c n',N,C)
+   \tkzLabelCircle[below=4pt,font=\scriptsize](A,C)(90){$(\alpha)$}
+   \tkzLabelCircle[left=4pt,font=\scriptsize](B,C)(-90){$(\beta)$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .6
+z.A     = point: new (0,0)
+z.B     = point: new (10,0)
+z.C     = point: new (4,0)
+C.AC    = circle: new (z.A,z.C)
+z.c,z.cp    = get_points (C.AC: tangent_at (z.C))
+z.M     = C.AC: point (1.2*math.pi)
+L.MC    = line: new (z.M,z.C)
+C.BC    = circle: new (z.B,z.C)
+z.N     = intersection (L.MC,C.BC)
+z.m,z.mp    = get_points (C.AC: tangent_at (z.M))
+z.n,z.np    = get_points (C.BC: tangent_at (z.N))
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(A,C B,C)
+\tkzDrawLines[new,add=1 and 1](M,m N,n C,c)
+\tkzDrawSegment(M,N)
+\tkzDrawPoints(A,B,C,M,N)
+\tkzLabelPoints[below right](A,B,C,M,N)
+\tkzFillAngles[blue!30,opacity=.3](m',M,C N,C,c' M,C,c n',N,C)
+\tkzLabelCircle[below=4pt,font=\scriptsize](A,C)(90){$(\alpha)$}
+\tkzLabelCircle[left=4pt,font=\scriptsize](B,C)(-90){$(\beta)$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Reim v2}
+% subsection reim_v2 (end)
+
+\subsection{Reim v3} % (fold)
+\label{sub:reim_v3}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A     = point: new (0,0)
+   z.B     = point: new (8,0)
+   z.C     = point: new (2,6)
+   L.AB    = line : new (z.A,z.B)
+   L.AC    = line : new (z.A,z.C)
+   L.BC    = line : new (z.B,z.C)
+   z.I     = L.BC : point (0.75)
+   z.J     = L.AC : point (0.4)
+   z.K     = L.AB : point (0.5)
+   T.AKJ   = triangle : new (z.A,z.K,z.J)
+   T.BIK   = triangle : new (z.B,z.I,z.K)
+   T.CIJ   = triangle : new (z.C,z.I,z.J)
+   z.x     = T.AKJ.circumcenter
+   z.y     = T.BIK.circumcenter
+   z.z     = T.CIJ.circumcenter
+   C.xK    = circle: new (z.x,z.K)
+   C.yK    = circle: new (z.y,z.K)
+   z.O,_   = intersection (C.xK,C.yK)
+   C.zO    = circle: new (z.z,z.O)
+   L.KO    = line: new (z.K,z.O)
+   z.D     = intersection (L.KO,C.zO)
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegments(K,D D,C)
+   \tkzDrawPolygon[teal](A,B,C)
+   \tkzDrawCircles[orange](x,A y,B z,C)
+   \tkzDrawPoints[fill=white](A,B,C,I,J,K,D)
+   \tkzLabelPoints[below](A,B,J,K,O)
+   \tkzLabelPoints[above](C,D,I)
+   \tkzDrawPoints[fill=black](O)
+   \tkzLabelCircle[below=4pt,font=\scriptsize](x,A)(20){$(\alpha)$}
+   \tkzLabelCircle[left=4pt,font=\scriptsize](y,B)(60){$(\beta)$}
+   \tkzLabelCircle[below=4pt,font=\scriptsize](z,C)(60){$(\gamma)$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale = 1.25
+   z.A     = point: new (0,0)
+   z.B     = point: new (8,0)
+   z.C     = point: new (2,6)
+   L.AB    = line : new (z.A,z.B)
+   L.AC    = line : new (z.A,z.C)
+   L.BC    = line : new (z.B,z.C)
+   z.I     = L.BC : point (0.75)
+   z.J     = L.AC : point (0.4)
+   z.K     = L.AB : point (0.5)
+   T.AKJ   = triangle : new (z.A,z.K,z.J)
+   T.BIK   = triangle : new (z.B,z.I,z.K)
+   T.CIJ   = triangle : new (z.C,z.I,z.J)
+   z.x     = T.AKJ.circumcenter
+   z.y     = T.BIK.circumcenter
+   z.z     = T.CIJ.circumcenter
+   C.xK    = circle: new (z.x,z.K)
+   C.yK    = circle: new (z.y,z.K)
+   z.O,_   = intersection (C.xK,C.yK)
+   C.zO    = circle: new (z.z,z.O)
+   L.KO    = line: new (z.K,z.O)
+   z.D     = intersection (L.KO,C.zO)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawSegments(K,D D,C)
+\tkzDrawPolygon[teal](A,B,C)
+\tkzDrawCircles[orange](x,A y,B z,C)
+\tkzDrawPoints[fill=white](A,B,C,I,J,K,D)
+\tkzLabelPoints[below](A,B,J,K,O)
+\tkzLabelPoints[above](C,D,I)
+\tkzDrawPoints[fill=black](O)
+\tkzLabelCircle[below=4pt,font=\scriptsize](x,A)(20){$(\alpha)$}
+\tkzLabelCircle[left=4pt,font=\scriptsize](y,B)(60){$(\beta)$}
+\tkzLabelCircle[below=4pt,font=\scriptsize](z,C)(60){$(\gamma)$}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Reim v3}
+% subsection reim_v3 (end)
+
+\subsection{Tangent and circle} % (fold)
+\label{sub:tangent_and_circle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A         = point:    new (1,0)
+   z.B         = point:    new (2,2)
+   z.E         = point:    new (5,-4)
+   L.AE        = line :    new (z.A,z.E)
+   C.AB        = circle:   new (z.A , z.B)
+   z.S         = C.AB.south
+   z.M         = L.AE.mid
+   L.Ti,L.Tj   = C.AB:   tangent_from (z.E)
+   z.i         = L.Ti.pb
+   z.j         = L.Tj.pb
+   z.k,z.l     = get_points (C.AB:  tangent_at (z.B))
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(A,B M,A)
+   \tkzDrawPoints(A,B,E,i,j,M,S)
+   \tkzDrawLines(E,i E,j k,l)
+   \tkzLabelPoints[right,font=\small](A,B,E,S,M)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A     = point:    new (1,0)
+z.B     = point:    new (2,2)
+z.E     = point:    new (5,-4)
+L.AE    = line :    new (z.A,z.E)
+C.AB    = circle:   new (z.A , z.B)
+z.S     = C.AB.south
+z.M     = L.AE.mid
+L.Ti,L.Tj   = C.AB:   tangent_from (z.E)
+z.i     = L.Ti.pb
+z.j     = L.Tj.pb
+z.k,z.l = get_points (C.AB:  tangent_at (z.B))
+\end{tkzelements}
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(A,B M,A)
+\tkzDrawPoints(A,B,E,i,j,M,S)
+\tkzDrawLines(E,i E,j k,l)
+\tkzLabelPoints[right,font=\small](A,B,E,S,M)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Tangent and circle}
+% subsection tangent_and_circle (end)
+
+\subsection{Homothety} % (fold)
+\label{sub:homothety}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point:  new (0,0)
+   z.B      = point:  new (1,2)
+   z.E      = point:  new (-3,2)
+   z.C,z.D  = z.E : set_homothety(2,z.A,z.B)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints(A,B,C,E,D)
+   \tkzLabelPoints(A,B,C,E)
+   \tkzDrawCircles(A,B C,D)
+   \tkzDrawLines(E,C E,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .6
+z.A  = point:  new (0,0)
+z.B  = point:  new (1,2)
+z.E  = point:  new (-3,2)
+z.C,z.D  = z.E : set_homothety(2,z.A,z.B)
+\end{tkzelements}
+\hspace*{\fill}\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(A,B,C,E,D)
+\tkzLabelPoints(A,B,C,E)
+\tkzDrawCircles(A,B C,D)
+\tkzDrawLines(E,C E,D)
+\end{tikzpicture}\hspace*{\fill}
+%\caption{Homothety}
+% subsection homothety (end)
+
+\subsection{Tangent and chord} % (fold)
+\label{sub:tangent_and_chord}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale       = .8
+   z.A         = point: new (0 , 0)
+   z.B         = point: new (6 , 0)
+   z.C         = point: new (1 , 5)
+   z.Bp        = point: new (2 , 0)
+   T.ABC       = triangle: new (z.A,z.B,z.C)
+   L.AB        = line: new (z.A,z.B)
+   z.O         = T.ABC.circumcenter
+   C.OA        = circle: new (z.O,z.A)
+   z.D         = C.OA: point (4.5)
+   L.AO        = line: new (z.A,z.O)
+   z.b1,z.b2   = get_points (C.OA: tangent_at (z.B))
+   z.H         = L.AB: projection (z.O)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircle(O,A)
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawSegments[new](A,O B,O O,H A,D D,B)
+   \tkzDrawLine(b1,b2)
+   \tkzDrawPoints(A,B,C,D,H,O)
+   \tkzFillAngles[green!20,opacity=.3](H,O,B A,C,B  A,B,b1)
+   \tkzFillAngles[teal!20,opacity=.3](B,D,A b2,B,A)
+   \tkzLabelPoints(A,B,C,D,H,O)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = 0.75
+z.A     = point: new (0 , 0)
+z.B     = point: new (6 , 0)
+z.C     = point: new (1 , 5)
+z.Bp    = point: new (2 , 0)
+T.ABC   = triangle: new (z.A,z.B,z.C)
+L.AB    = line: new (z.A,z.B)
+z.O     = T.ABC.circumcenter
+C.OA    = circle: new (z.O,z.A)
+z.D     = C.OA: point (4.5)
+L.AO    = line: new (z.A,z.O)
+z.b1,z.b2   = get_points (C.OA: tangent_at (z.B))
+z.H     = L.AB: projection (z.O)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircle(O,A)
+\tkzDrawPolygon(A,B,C)
+\tkzDrawSegments[new](A,O B,O O,H A,D D,B)
+\tkzDrawLine(b1,b2)
+\tkzDrawPoints(A,B,C,D,H,O)
+\tkzFillAngles[green!20,opacity=.3](H,O,B A,C,B  A,B,b1)
+\tkzFillAngles[teal!20,opacity=.3](B,D,A b2,B,A)
+\tkzLabelPoints(A,B,C,D,H,O)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Tangent and chord}
+% subsection tangent_and_chord (end)
+
+
+\subsection{Three chords} % (fold)
+\label{sub:three_chords}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.O      = point: new (0 , 0)
+   z.B      = point: new (0 , 2)
+   z.P      = point: new (1 , -.5)
+   C.OB     = circle : new (z.O,z.B)
+   C.PB     = circle : new (z.P,z.B)
+   _,z.A    = intersection (C.OB,C.PB)
+   z.D      = C.PB: point(math.pi/3)
+   z.C      = C.PB: point(-math.pi/3)
+   z.E      = C.OB: point(-math.pi/180*50)
+   L.AB     = line : new (z.A,z.B)
+   L.CD     = line : new (z.C,z.D)
+   z.G      = intersection (L.AB,L.CD)
+   L.GE     = line : new (z.G,z.E)
+   z.F,_    = intersection (L.GE,C.OB)
+   T.CDE    = triangle: new (z.C,z.D,z.E)
+   T.BFD    = triangle: new (z.B,z.F,z.D)
+   z.w      = T.CDE.circumcenter
+   z.x      = T.BFD.circumcenter
+   L.GB     = line : new (z.G,z.B)
+   L.GE     = line : new (z.G,z.E)
+   L.GD     = line : new (z.G,z.D)
+   C.xB     = circle : new (z.x,z.B)
+   C.xF     = circle : new (z.x,z.F)
+   C.xD     = circle : new (z.x,z.D)
+   z.Ap     = intersection (L.GB,C.xB)
+   z.Ep     = intersection (L.GE,C.xF)
+   z.Cp     = intersection (L.GD,C.xD)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(O,B)
+   \tkzDrawCircles[cyan](P,B)
+   \tkzDrawCircles[red](w,E)
+   \tkzDrawCircles[new](x,F)
+   \tkzDrawSegments(A,G E,G C,G)
+   \tkzDrawPolygons[new](A,E,C A',E',C')
+   \tkzDrawPoints(A,...,G,A',E',C',O,P)
+   \begin{scope}[font=\scriptsize]
+   \tkzLabelPoints(A,...,F)
+   \tkzLabelPoints[above left](G,A',E',C')
+   \tkzLabelCircle[left](O,B)(30){$(\beta)$}
+   \tkzLabelCircle[below](P,A)(40){$(\gamma)$}
+   \tkzLabelCircle[right](w,C)(90){$(\alpha)$}
+   \tkzLabelCircle[left](x,B)(-230){$((\delta))$}
+   \end{scope}
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.O  = point: new (0 , 0)
+z.B  = point: new (0 , 2)
+z.P  = point: new (1 , -.5)
+C.OB = circle : new (z.O,z.B)
+C.PB = circle : new (z.P,z.B)
+_,z.A    = intersection (C.OB,C.PB)
+z.D  = C.PB: point(math.pi/3)
+z.C  = C.PB: point(-math.pi/3)
+z.E  = C.OB: point(-math.pi/180*50)
+L.AB = line : new (z.A,z.B)
+L.CD = line : new (z.C,z.D)
+z.G  = intersection (L.AB,L.CD)
+L.GE = line : new (z.G,z.E)
+z.F,_    = intersection (L.GE,C.OB)
+T.CDE    = triangle: new (z.C,z.D,z.E)
+T.BFD    = triangle: new (z.B,z.F,z.D)
+z.w  = T.CDE.circumcenter
+z.x  = T.BFD.circumcenter
+L.GB = line : new (z.G,z.B)
+L.GE = line : new (z.G,z.E)
+L.GD = line : new (z.G,z.D)
+C.xB = circle : new (z.x,z.B)
+C.xF = circle : new (z.x,z.F)
+C.xD = circle : new (z.x,z.D)
+z.Ap = intersection (L.GB,C.xB)
+z.Ep,_   = intersection (L.GE,C.xF)
+z.Cp,_   = intersection (L.GD,C.xD)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(O,B)
+\tkzDrawCircles[cyan](P,B)
+\tkzDrawCircles[red](w,E)
+\tkzDrawCircles[new](x,F)
+\tkzDrawSegments(A,G E,G C,G)
+\tkzDrawPolygons[new](A,E,C A',E',C')
+\tkzDrawPoints(A,...,G,A',E',C',O,P)
+\begin{scope}[font=\scriptsize]
+   \tkzLabelPoints(A,...,F)
+   \tkzLabelPoints[above left](G,A',E',C')
+   \tkzLabelCircle[left](O,B)(30){$(\beta)$}
+   \tkzLabelCircle[below](P,A)(40){$(\gamma)$}
+   \tkzLabelCircle[right](w,C)(90){$(\alpha)$}
+   \tkzLabelCircle[left](x,B)(-230){$((\delta))$}
+\end{scope}
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Three chords}
+% subsection three_chords (end)
+
+\subsection{Three tangents} % (fold)
+\label{sub:three_tangents}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A    = point: new (-1 , 0)
+   z.C    = point: new (4 , -1.5)
+   z.E    = point: new (1 , -1)
+   z.F    = point: new (1.5 , 2.5)
+   T.AEF  = triangle : new (z.A,z.E,z.F)
+   T.CEF  = triangle : new (z.C,z.E,z.F)
+   z.w    = T.AEF.circumcenter
+   z.x    = T.CEF.circumcenter
+   C.wE   = circle : new (z.w,z.E)
+   C.xE   = circle : new (z.x,z.E)
+   L.Aw   = line : new (z.A,z.w)
+   L.Cx   = line : new (z.C,z.x)
+   z.G    = intersection (L.Aw,L.Cx)
+   L.TA   = C.wE : tangent_at (z.A)
+   L.TC   = C.xE : tangent_at (z.C)
+   z.I    = intersection (L.TA,L.TC)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(w,E)
+   \tkzDrawCircles[cyan](x,E)
+   \tkzDrawCircles[red](G,A)
+   \tkzDrawLines(A,I C,I F,I)
+   \tkzDrawPoints(A,C,E,F)
+   \tkzLabelPoints[right](A)
+   \tkzLabelPoints[above right](E,F)
+   \tkzLabelPoints[below](C)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale  = .75
+z.A    = point: new (-1 , 0)
+z.C    = point: new (4 , -1.5)
+z.E    = point: new (1 , -1)
+z.F    = point: new (1.5 , 2.5)
+T.AEF  = triangle : new (z.A,z.E,z.F)
+T.CEF  = triangle : new (z.C,z.E,z.F)
+z.w    = T.AEF.circumcenter
+z.x    = T.CEF.circumcenter
+C.wE   = circle : new (z.w,z.E)
+C.xE   = circle : new (z.x,z.E)
+L.Aw   = line : new (z.A,z.w)
+L.Cx   = line : new (z.C,z.x)
+z.G    = intersection (L.Aw,L.Cx)
+L.TA   = C.wE : tangent_at (z.A)
+L.TC   = C.xE : tangent_at (z.C)
+z.I    = intersection (L.TA,L.TC)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(w,E)
+\tkzDrawCircles[cyan](x,E)
+\tkzDrawCircles[red](G,A)
+\tkzDrawLines(A,I C,I F,I)
+\tkzDrawPoints(A,C,E,F)
+\tkzLabelPoints[right](A)
+\tkzLabelPoints[above right](E,F)
+\tkzLabelPoints[below](C)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Three tangents}
+% subsection three_tangents (end)
+
+\subsection{Midarc} % (fold)
+\label{sub:midarc}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A   = point:  new (-1,0)
+   z.B   = point:  new (2,4)
+   C.AB  = circle: new (z.A,z.B)
+   z.C   =  z.A: rotation (math.pi/3,z.B)
+   z.D   = C.AB: midarc (z.B,z.C)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints(A,B,C)
+   \tkzDrawCircles(A,B)
+   \tkzDrawPoints(A,...,D)
+   \tkzLabelPoints(A,...,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .5
+z.A  = point:  new (-1,0)
+z.B  = point:  new (2,4)
+C.AB = circle:  new (z.A,z.B)
+z.C =  z.A: rotation (math.pi/3,z.B)
+z.D = C.AB: midarc (z.B,z.C)
+\end{tkzelements}
+
+\hspace*{\fill}\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPoints(A,B,C)
+\tkzDrawCircles(A,B)
+\tkzDrawPoints(A,...,D)
+\tkzLabelPoints(A,...,D)
+\end{tikzpicture}\hspace*{\fill}
+%\caption{Midarc}
+% subsection midarc (end)
+
+\subsection{Lemoine Line without macro} % (fold)
+\label{sub:lemoine_line_without_macro}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale       = 1.6
+   z.A         = point: new (1,0)
+   z.B         = point: new (5,2)
+   z.C         = point: new (1.2,2)
+   T           = triangle: new(z.A,z.B,z.C)
+   z.O         = T.circumcenter
+   L.AB        = line: new (z.A,z.B)
+   L.AC        = line: new (z.A,z.C)
+   L.BC        = line: new (z.B,z.C)
+   C.OA        = circle: new (z.O,z.A)
+   z.Ar,z.Al   = get_points (C.OA: tangent_at (z.A))
+   z.Br,z.Bl   = get_points (C.OA: tangent_at (z.B))
+   z.Cr,z.Cl   = get_points (C.OA: tangent_at (z.C))
+   L.tA        = line: new (z.Ar,z.Al)
+   L.tB        = line: new (z.Br,z.Bl)
+   L.tC        = line: new (z.Cr,z.Cl)
+   z.P         = intersection (L.tA,L.BC)
+   z.Q         = intersection (L.tB,L.AC)
+   z.R         = intersection (L.tC,L.AB)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon[teal](A,B,C)
+   \tkzDrawCircle(O,A)
+   \tkzDrawPoints(A,B,C,P,Q,R)
+   \tkzLabelPoints(A,B,C,P,Q,R)
+   \tkzDrawLine[blue](Q,R)
+   \tkzDrawLines[red](Ar,Al Br,Q Cr,Cl)
+   \tkzDrawSegments(A,R C,P C,Q)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale       = 0.75
+z.A         = point: new (1,0)
+z.B         = point: new (5,2)
+z.C         = point: new (1.2,2)
+T           = triangle: new(z.A,z.B,z.C)
+z.O         = T.circumcenter
+L.AB        = line: new (z.A,z.B)
+L.AC        = line: new (z.A,z.C)
+L.BC        = line: new (z.B,z.C)
+C.OA        = circle: new (z.O,z.A)
+z.Ar,z.Al   = get_points (C.OA: tangent_at (z.A))
+z.Br,z.Bl   = get_points (C.OA: tangent_at (z.B))
+z.Cr,z.Cl   = get_points (C.OA: tangent_at (z.C))
+L.tA        = line: new (z.Ar,z.Al)
+L.tB        = line: new (z.Br,z.Bl)
+L.tC        = line: new (z.Cr,z.Cl)
+z.P         = intersection (L.tA,L.BC)
+z.Q         = intersection (L.tB,L.AC)
+z.R         = intersection (L.tC,L.AB)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon[teal](A,B,C)
+\tkzDrawCircle(O,A)
+\tkzDrawPoints(A,B,C,P,Q,R)
+\tkzLabelPoints(A,B,C,P,Q,R)
+\tkzDrawLine[blue](Q,R)
+\tkzDrawLines[red](Ar,Al Br,Q Cr,Cl)
+\tkzDrawSegments(A,R C,P C,Q)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Lemoine Line without macro}
+% subsection lemoine_line_without_macro (end)
+
+\subsection{First Lemoine circle} % (fold)
+\label{sub:first_lemoine_circle}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.A      = point:  new (1,1)
+   z.B      = point:  new (5,1)
+   z.C      = point:  new (2,3)
+   T        = triangle: new (z.A,z.B,z.C)
+   z.O      = T.circumcenter
+   z.o,z.w  = get_points (T : first_lemoine_circle ())
+   z.L      = T : lemoine_point ()
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(A,B,C)
+   \tkzDrawPoints(A,B,C,o,w,O,L)
+   \tkzLabelPoints(A,B,C,o,w,O,L)
+   \tkzDrawCircles(o,w  O,A)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.A      = point:  new (1,1)
+z.B      = point:  new (5,1)
+z.C      = point:  new (2,3)
+T        = triangle: new (z.A,z.B,z.C)
+z.O      = T.circumcenter
+z.o,z.w  = get_points (T : first_lemoine_circle ())
+z.L      = T : lemoine_point ()
+\end{tkzelements}
+
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(A,B,C)
+\tkzDrawPoints(A,B,C,o,w,O,L)
+\tkzLabelPoints(A,B,C,o,w,O,L)
+\tkzDrawCircles(o,w  O,A)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{First Lemoine circle}
+% subsection first_lemoine_circle (end)
+
+\subsection{First and second Lemoine circles} % (fold)
+\label{sub:first_and_second_lemoine_circles}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale             = 2
+   z.a               = point:  new (0,0)
+   z.b               = point:  new (5,0)
+   z.c               = point:  new (2,3)
+   T                 = triangle: new (z.a,z.b,z.c)
+   z.O               = T.circumcenter
+   z.o,z.p           = get_points (T : first_lemoine_circle ())
+   L.ab              = line : new (z.a,z.b)
+   L.ac              = line : new (z.a,z.c)
+   L.bc              = line : new (z.b,z.c)
+   z.L,z.x           = get_points (T : second_lemoine_circle ())
+   C.first_lemoine   = circle : new (z.o,z.p)
+   z.y1,z.y2         = intersection (L.ab,C.first_lemoine)
+   z.y5,z.y6         = intersection (L.bc,C.first_lemoine)
+   z.y3,z.y4         = intersection (L.ac,C.first_lemoine)
+   C.second_lemoine  = circle : new (z.L,z.x)
+   z.x1,z.x2         = intersection (L.ab,C.second_lemoine)
+   z.x3,z.x4         = intersection (L.bc,C.second_lemoine)
+   z.x5,z.x6         = intersection (L.ac,C.second_lemoine)
+   L.y1y6            = line : new (z.y1,z.y6)
+   L.y4y5            = line : new (z.y4,z.y5)
+   L.y2y3            = line : new (z.y2,z.y3)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(a,b,c y1,y2,y3,y4,y5,y6)
+   \tkzDrawPoints(x1,x2,x3,x4,x5,x6,L)
+   \tkzDrawPoints(a,b,c,o,O,y1,y2,y3,y4,y5,y6)
+   \tkzLabelPoints[below right](a,b,c,o,O,y1,y2,y3,y4,y5,y6)
+   \tkzLabelPoints[below left](x1,x2,x3,x4,x5,x6)
+   \tkzLabelPoints[above](L)
+   \tkzDrawCircles(L,x o,p O,a)
+   \tkzDrawSegments(L,O x1,x4 x2,x5 x3,x6)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale     = 2
+z.a   = point:  new (0,0)
+z.b   = point:  new (5,0)
+z.c   = point:  new (2,3)
+T     = triangle: new (z.a,z.b,z.c)
+z.O   = T.circumcenter
+z.o,z.p   = get_points (T : first_lemoine_circle ())
+L.ab      = line : new (z.a,z.b)
+L.ac      = line : new (z.a,z.c)
+L.bc      = line : new (z.b,z.c)
+z.L,z.x   = get_points (T : second_lemoine_circle ())
+C.first_lemoine   = circle : new (z.o,z.p)
+z.y1,z.y2     = intersection (L.ab,C.first_lemoine)
+z.y5,z.y6     = intersection (L.bc,C.first_lemoine)
+z.y3,z.y4     = intersection (L.ac,C.first_lemoine)
+C.second_lemoine  = circle : new (z.L,z.x)
+z.x1,z.x2     = intersection (L.ab,C.second_lemoine)
+z.x3,z.x4     = intersection (L.bc,C.second_lemoine)
+z.x5,z.x6     = intersection (L.ac,C.second_lemoine)
+L.y1y6    = line : new (z.y1,z.y6)
+L.y4y5    = line : new (z.y4,z.y5)
+L.y2y3    = line : new (z.y2,z.y3)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(a,b,c y1,y2,y3,y4,y5,y6)
+\tkzDrawPoints(x1,x2,x3,x4,x5,x6,L)
+\tkzDrawPoints(a,b,c,o,O,y1,y2,y3,y4,y5,y6)
+\tkzLabelPoints[below right](a,b,c,o,O,y1,y2,y3,y4,y5,y6)
+\tkzLabelPoints[below left](x1,x2,x3,x4,x5,x6)
+\tkzLabelPoints[above](L)
+\tkzDrawCircles(L,x o,p O,a)
+\tkzDrawSegments(L,O x1,x4 x2,x5 x3,x6)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{First and second Lemoine circles}
+% subsection first_and_second_lemoine_circles (end)
+
+\subsection{Inversion} % (fold)
+\label{sub:inversion}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+ \begin{tkzelements}
+   z.A         = point: new (-1,0)
+   z.B         = point: new (2,2)
+   z.C         = point: new (2,4)
+   z.E         = point: new (1,6)
+   C.AC        = circle:    new (z.A,z.C)
+   L.Tt1,L.Tt2 = C.AC: tangent_from (z.E)
+   z.t1        = L.Tt1.pb
+   z.t2        = L.Tt2.pb
+   L.AE        = line: new (z.A,z.E)
+   z.H         = L.AE : projection (z.t1)
+   z.Bp,
+   z.Ep,
+   z.Cp        = C.AC: set_inversion ( z.B, z.E, z.C )
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPoints(A,B,C)
+   \tkzDrawCircles(A,C A,B)
+   \tkzDrawLines(A,B' E,t1 E,t2 t1,t2 A,E)
+   \tkzDrawPoints(A,B,C,E,t1,t2,H,B',E')
+   \tkzLabelPoints(A,B,C,E,t1,t2,B',E')
+   \tkzLabelPoints[above](C')
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+scale = .75
+z.A     = point: new (-1,0)
+z.B     = point: new (2,2)
+z.C     = point: new (2,4)
+z.E     = point: new (1,6)
+C.AC    = circle:    new (z.A,z.C)
+L.Tt1,L.Tt2 = C.AC: tangent_from (z.E)
+z.t1    = L.Tt1.pb
+z.t2    = L.Tt2.pb
+L.AE    = line: new (z.A,z.E)
+z.H     = L.AE : projection (z.t1)
+z.Bp,
+z.Ep,
+z.Cp    = C.AC: set_inversion ( z.B, z.E, z.C )
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawPoints(A,B,C)
+  \tkzDrawCircles(A,C A,B)
+  \tkzDrawLines(A,B' E,t1 E,t2 t1,t2 A,E)
+  \tkzDrawPoints(A,B,C,E,t1,t2,H,B',E')
+  \tkzLabelPoints(A,B,C,E,t1,t2,B',E')
+  \tkzLabelPoints[above](C')
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Inversion}
+% subsection inversion (end)
+
+\subsection{Gergonne point} % (fold)
+\label{sub:gergonne_point}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+    z.a  = point: new(1,0)
+    z.b  = point: new(6,2)
+    z.c  = point: new(2,5)
+    T    = triangle : new (z.a,z.b,z.c)
+    z.g  = T : gergonne_point ()
+    z.i  = T.incenter
+    z.ta,z.tb,z.tc = get_points (T :  intouch ())
+end{elements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(a,b,c)
+   \tkzDrawPoints(a,b,c,g)
+   \tkzLabelPoints(a,b,c)
+   \tkzDrawSegments (a,ta b,tb c,tc)
+   \tkzDrawCircle(i,ta)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.a  = point: new(1,0)
+z.b  = point: new(6,2)
+z.c  = point: new(2,5)
+T    = triangle : new (z.a,z.b,z.c)
+z.g  = T : gergonne_point ()
+z.i  = T.incenter
+z.ta,z.tb,z.tc = get_points (T :  intouch ())
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(a,b,c)
+\tkzDrawPoints(a,b,c,g)
+\tkzLabelPoints(a,b,c)
+\tkzDrawSegments (a,ta b,tb c,tc)
+\tkzDrawCircle(i,ta)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Gergonne point}
+% subsection gergonne_point (end)
+
+\subsection{Antiparallel through Lemoine point} % (fold)
+\label{sub:antiparallel_through_lemoine_point}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   z.a         = point:  new (0,0)
+   z.b         = point:  new (5,0)
+   z.c         = point:  new (1,4)
+   T           = triangle: new (z.a,z.b,z.c)
+   z.L         = T : lemoine_point ()
+   L.anti      = T : antiparallel (z.L,0)
+   z.x_0,z.x_1 = get_points (L.anti)
+   L.anti      = T : antiparallel (z.L,1)
+   z.y_0,z.y_1 = get_points (L.anti)
+   L.anti      = T : antiparallel (z.L,2)
+   z.z_0,z.z_1 = get_points (L.anti)
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygons(a,b,c)
+   \tkzDrawPoints(a,b,c,L,x_0,x_1,y_0,y_1,z_0,z_1)
+   \tkzLabelPoints(a,b)
+   \tkzLabelPoints[above](L,c)
+   \tkzDrawSegments(x_0,x_1 y_0,y_1 z_0,z_1)
+   \tkzDrawCircle(L,x_0)
+\end{tikzpicture}
+\end{tkzexample}
+
+\begin{tkzelements}
+z.a = point:  new (0,0)
+z.b = point:  new (5,0)
+z.c = point:  new (1,4)
+T = triangle: new (z.a,z.b,z.c)
+z.L = T : lemoine_point ()
+L.anti = T : antiparallel (z.L,0)
+z.x_0,z.x_1 = get_points (L.anti)
+L.anti = T : antiparallel (z.L,1)
+z.y_0,z.y_1 = get_points (L.anti)
+L.anti = T : antiparallel (z.L,2)
+z.z_0,z.z_1 = get_points (L.anti)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(a,b,c)
+\tkzDrawPoints(a,b,c,L,x_0,x_1,y_0,y_1,z_0,z_1)
+\tkzLabelPoints(a,b)
+\tkzLabelPoints[above](L,c)
+\tkzDrawSegments(x_0,x_1 y_0,y_1 z_0,z_1)
+\tkzDrawCircle(L,x_0)
+\end{tikzpicture}
+\hspace*{\fill}
+%\caption{Antiparallels}
+% subsection antiparallel_through_lemoine_point (end)
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-howtouse.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-howtouse.tex
new file mode 100644
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--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-howtouse.tex
@@ -0,0 +1,193 @@
+\newpage
+\section{How to use} % (fold)
+\label{sec:how_to_use}
+
+You need to load either \TIKZ{} or \pkg{tkz-euclide} if you want to use these packages to get your plots, then you need to load \pkg{tkz-elements}.
+
+Loading \pkg{tkz-elements} allows you to use the \env{elements} environment. However, you can use the macro \tkzcname{directlua} or the \env{luacode} environment  (the package \pkg{luacode} is loaded automatically).
+
+
+\subsection{Environment elements} % (fold)
+\label{sub:environment_elements}
+
+You must first create an environment \tkzNameEnv{tkzelements}, then in this environment you create the fixed points of your figure. (For the moment, you place the environment \env{elements} before the environment \env{tikzpicture} but it is possible to place it inside the latter.)
+
+In the following example, three fixed points are used (lines 8, 9 and 10), the first object \tkzNameObj{point} $A$ is created by 
+
+|z.A  = point: new (2 , 4)|. 
+
+Then we create a \tkzNameObj{triangle} (line 11)
+
+|T.ABC  = triangle: new (z.A,z.B,z.C)|
+
+Once the triangle has been created, you can either use its attributes or a method associated with the triangle object. In all cases, the result is either a number or a new object.
+
+In order to obtain the circle inscribed in this triangle, we use a method of the \tkzname{triangle}. We obtain a new object, a circle, which I call |C.Ii|. A circle is defined by its center and a point through which it passes.  $I$ is the center and $i$ is the  projection of this center on the  side opposed to the first point of the triangle. 
+
+There are several ways of obtaining these two points. As in the example, |get_points| is a function that extracts the points from the object given as an argument. You can also use the circle attributes: |z.I = C.Ii.center| and |z.i = CIi.through|. The first method is obviously simpler, but less explicit. Another possibility would be to obtain the center as an attribute of the triangle |z.I = T.ABC.incircle| and then project this center onto one of the sides, for example |z.i = T.ABC.bc : projection (z.I)|. An explanation is in order: |T.ABC.bc | is the straight line defined by the last two points of the triangle (see triangle attributes \ref{sec:classe_triangle}).
+
+Then we look for the  circumscribed circle, which is obtained using a method of the triangle object. We define the circumscribed \tkzNameObj{circle} named |C.WA|.
+
+|C.WA   = T.ABC : circum_circle ()| (line 16)
+
+| z.W,_   = get_points (C.WA)| is used to get the center but possible is
+
+ |z.W = T.ABC.circumcircle|
+
+The south pole of the circle with center $W$ passing through $A$ is given by an attribute of the object \tkzNameObj{circle}.
+
+We finally look for the intersection of two lines.
+
+Line 17 an object line is created. Line 18 I name a line object already created (it's a triangle attribute).
+
+All points are defined and stored in the |z| table. The macro \tkzcname{tkzGetNodes} retrieves the keys and associated values from this table and creates the nodes to be used by \TIKZ\ or \pkg{tkz-euclide}.
+
+\begin{tkzexample}[small,code only,num]
+% !TEX TS-program = lualatex
+\documentclass{article}
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document}
+
+\begin{tkzelements}
+   z.A     = point: new (2 , 4)
+   z.B     = point: new (0 , 0)
+   z.C     = point: new (8 , 0)
+   T.ABC   = triangle: new (z.A,z.B,z.C)
+   C.Ii    = T.ABC: in_circle ()
+   z.I,z.i = get_points (C.Ii)
+   C.WA    = T.ABC : circum_circle ()
+   z.W,_   = get_points (C.WA)
+   z.O     = C.WA.south
+   L.AO    = line: new (z.A,z.O)
+   L.BC    = T.ABC.bc
+   z.I_A   = intersection (L.AO,L.BC)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(W,A I,i)
+   \tkzDrawArc(O,C)(B)
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawSegments[new](A,O B,O C,O)
+   \tkzDrawLine(B,I)
+   \tkzDrawPoints(A,B,C,I,I_A,W,O)
+   \tkzFillAngles[green!20,opacity=.3](A,O,B A,C,B)
+   \tkzFillAngles[teal!20,opacity=.3](O,B,C B,C,O B,A,O O,A,C)
+   \tkzLabelPoints(I,I_A,W,B,C)
+   \tkzLabelPoints[above](A)
+\end{tikzpicture}
+\end{document}
+\end{tkzexample}
+
+\begin{tkzelements}
+   scale =.75
+   z.A     = point: new (2 , 4)
+   z.B     = point: new (0 , 0)
+   z.C     = point: new (8 , 0)
+   T.ABC   = triangle: new (z.A,z.B,z.C)
+   C.Ii    = T.ABC: in_circle ()
+   z.I,z.i = get_points (C.Ii)
+   C.WA    = T.ABC : circum_circle ()
+   z.W,_   = get_points (C.WA)
+   z.O     = C.WA.south
+   L.AO    = line: new (z.A,z.O)
+   L.BC    = T.ABC.bc
+   z.I_A   = intersection (L.AO,L.BC)
+\end{tkzelements}
+
+\hspace*{\fill}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(W,A I,i)
+\tkzDrawArc(O,C)(B)
+\tkzDrawPolygon(A,B,C)
+\tkzDrawSegments[new](A,O B,O C,O)
+\tkzDrawLine(B,I)
+\tkzDrawPoints(A,B,C,I,I_A,W,O)
+\tkzFillAngles[green!20,opacity=.3](A,O,B A,C,B)
+\tkzFillAngles[teal!20,opacity=.3](O,B,C B,C,O B,A,O O,A,C)
+\tkzLabelPoints(I,I_A,W,B,C,O)
+\tkzLabelPoints[above](A)
+\end{tikzpicture}
+\hspace*{\fill}
+% subsection environment_elements (end)
+
+\subsection{Fom Lua to tkz-euclide or TikZ} % (fold)
+\label{sub:fom_lua_to_tkz_euclide_or_tikz}
+
+\subsubsection{Points transfer} % (fold)
+\label{ssub:points_transfer}
+We use an environment \tkzname{elements}  outside an environment \tkzname{tikzpicture} which allows us to carry out all the necessary calculations, then we launch the macro \tkzcname{tkzGetNodes} which transforms the affixes of the table \tkzname{z} into a list of \tkzname{Nodes}. It only remains to draw.
+
+Currently the drawing program is either \TIKZ\ or \pkg{tkz-euclide}. You have the possibility to use another package to trace but for that you have to create a macro similar to \tkzcname{tkzGetNodes}. Of course, this package must be able to store the points as does \TIKZ\ or \pkg{tkz-euclide}. 
+
+\vspace*{1em}
+
+\begin{tkzexample}[latex=0cm,small,code only]
+\def\tkzGetNodes{\directlua{%
+   for K,V in pairs(z) do
+      local KS,n,sd,ft
+      KS = tostring(K)
+      n = string.len(KS)
+      if n >1 then
+      _,_,ft, sd = string.find( KS , "(.+)(.)" )  
+     if sd == "p" then   K=ft.."'" end  
+       end    
+  tex.print("\\coordinate ("..K..") at ("..V.re..","..V.im..") ;\\\\")
+end}
+}
+\end{tkzexample}
+
+The environment \tkzNameEnv{elements} allows to use the underscore |_| and the macro \tkzcname{tkzGetNodes} allows to obtain names of nodes containing \tkzname{prime}. (see the next example)
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[latex=0cm,small,code only]
+\begin{tkzelements}
+   scale = 1.2
+   z.o   = point: new (0,0)
+   z.a_1 = point: new (2,1)
+   z.a_2 = point: new (1,2)
+   z.ap  = z.a_1 + z.a_2
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegments(o,a_1 o,a_2 o,a')
+   \tkzDrawSegments[red](a_1,a' a_2,a')
+   \tkzDrawPoints(a_1,a_2,a',o)
+   \tkzLabelPoints(o,a_1,a_2,a')
+\end{tikzpicture}
+\end{tkzexample}%
+\end{minipage}%
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+scale = 1.2
+z.o = point: new (0,0)
+z.a_1 = point: new (2,1)
+z.a_2 = point: new (1,2)
+z.ap = z.a_1 + z.a_2
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+ \tkzDrawSegments(o,a_1 o,a_2 o,a')
+ \tkzDrawSegments[red](a_1,a' a_2,a')
+ \tkzDrawPoints(a_1,a_2,a',o)
+ \tkzLabelPoints(o,a_1,a_2,a')
+\end{tikzpicture}
+\end{minipage}%
+
+% subsection fom_lua_to_tkz_euclide_or_tikz (end)
+\subsubsection{Other transfers} % (fold)
+\label{ssub:other_transfers}
+
+Sometimes it's useful to transfer angle or length measurements. For this purpose, I have created the function (see \ref{ssub:transfer_from_lua_to_tex})  
+\Igfct{package}{set\_lua\_to\_tex (list)}
+
+% subsubsection other_transfers (end)
+% subsubsection points_transfer (end)
+
+% section how_to_use (end)
+
+
+
+
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-intersection.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-intersection.tex
new file mode 100644
index 00000000000..db290e34477
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-intersection.tex
@@ -0,0 +1,315 @@
+\newpage
+\section{Intersections} % (fold)
+\label{sec:intersections}
+
+It's an essential tool. For the moment, the classes concerned are lines, circles and ellipses, with the following combinations: line-line; line-circle; circle-circle and line-ellipse. The argument is a pair of objects, in any order.
+Results consist of one or two values, either points, boolean \tkzname{false} or underscore |_|. 
+
+\subsection{Line-line} % (fold)
+\label{sub:line_line}
+
+The result is of the form: |point| or |false|.
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A   = point : new (1,-1)
+   z.B   = point : new (4,1)
+   z.C   = point : new (2,1)
+   z.D   = point : new (4,-2) 
+    z.I  = point : new (0,0)
+   L.AB  = line : new (z.A,z.B)
+   L.CD  = line : new (z.C,z.D)
+   x     = intersection (L.AB,L.CD)
+   if x  == false then 
+   tex.print('error')
+   else 
+   z.I   = x
+   end
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegments(A,B C,D)
+   \tkzDrawPoints(A,B,C,D,I)
+   \tkzLabelPoints(A,B,C,D,I)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+z.A   = point : new (1,-1)
+z.B   = point : new (4,1)
+z.C   = point : new (2,1)
+z.D   = point : new (4,-2) 
+ z.I  = point : new (0,0)
+L.AB  = line : new (z.A,z.B)
+L.CD  = line : new (z.C,z.D)
+x = intersection (L.AB,L.CD)
+if x  == false then 
+tex.print('error')
+else 
+z.I   = x
+end
+\end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawSegments(A,B C,D)
+   \tkzDrawPoints(A,B,C,D,I)
+   \tkzLabelPoints(A,B,C,D,I)
+\end{tikzpicture}
+\end{minipage}
+
+Other examples: \ref{ssub:altshiller}, \ref{ssub:lemoine}, \ref{sub:alternate}, \ref{sub:environment_elements}
+% subsection line_line (end)
+
+\newpage
+\subsection{Line-circle} % (fold)
+\label{sub:line_circle}
+The result is of the form : |point,point| or |false,false|. If the line is tangent to the circle, then the two points are identical. You can ignore one of the points by using the underscore: |_,point| or |point,_|. When the intersection yields two solutions, the order of the points is determined by the argument of |(z.p - z.c)| with |c| center of the circle and |p| point of intersection. The first solution corresponds to the smallest argument (arguments are between 0 and $2\pi$).
+
+\begin{minipage}{0.6\textwidth}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A   = point : new (1,-1)
+   z.B   = point : new (1,2)
+   L.AB  = line : new (z.A,z.B)
+   z.O   = point : new (2,1)
+   z.D   = point : new (3,1)
+   z.E   = point : new (3,2)
+   L.AE  = line : new (z.A,z.E)
+   C.OD  = circle : new (z.O,z.D)
+   z.I,_ = intersection (L.AB,C.OD)
+   _,z.K = intersection (C.OD,L.AE)
+\end{tkzelements}
+
+\begin{tikzpicture}
+\tkzGetNodes
+   \tkzDrawLines(A,B A,E)
+   \tkzDrawCircle(O,D)
+   \tkzDrawPoints(A,B,O,D,I,K)
+   \tkzLabelPoints[left](A,B,O,D,I,K)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.4\textwidth}
+\begin{tkzelements}
+   scale = 2
+z.A = point : new (1,-1)
+z.B = point : new (1,2)
+L.AB = line : new (z.A,z.B)
+z.O = point : new (2,1)
+z.D = point : new (3,1)
+z.E = point : new (3,2)
+L.AE = line : new (z.A,z.E)
+C.OD = circle : new (z.O,z.D)
+z.I,_ = intersection (L.AB,C.OD)
+_,z.K = intersection (C.OD,L.AE)
+\end{tkzelements}
+
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawLines(A,B A,E)
+\tkzDrawCircle(O,D)
+\tkzDrawPoints(A,B,O,D,I,K)
+\tkzLabelPoints[left](A,B,O,D,I,K)
+\end{tikzpicture}
+\end{minipage}
+
+Other examples: \ref{ssub:altshiller}
+% subsection line_circle (end)
+
+\newpage
+\subsection{Circle-circle} % (fold)
+\label{sub:circle_circle}
+
+The result is of the form : |point,point| or |false,false|. If the circles are  tangent, then the two points are identical. You can ignore one of the points by using the underscore: |_ , point| or |point , _|. As for the intersection of a line and a circle, consider the argument of |z.p-z.c|  with |c| center of the first circle and |p| point of intersection. The first solution corresponds to the smallest argument (arguments are between 0 and $2\pi$).
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[small,code only]
+\begin{tkzelements}
+   z.A      = point : new (1,1)
+   z.B      = point : new (2,2)
+   z.C      = point : new (3,3)
+   z.D      = point : new (3,0)
+   C.AB     = circle : new (z.A,z.B)
+   C.CB     = circle : new (z.C,z.B)
+   z.I,_    = intersection (C.AB,C.CB)
+   C.DC     = circle : new (z.D,z.C)
+   z.J,z.K  = intersection (C.DC,C.CB)
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawCircles(A,B C,B D,C)
+   \tkzDrawPoints(A,I,C,D,J,K)
+   \tkzLabelPoints(A,I,C,D,J,K)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+z.A = point : new (1,1)
+z.B = point : new (2,2)
+z.C = point : new (3,3)
+z.D = point : new (3,0)
+C.AB = circle : new (z.A,z.B)
+C.CB = circle : new (z.C,z.B)
+z.I,_ = intersection (C.AB,C.CB)
+C.DC = circle : new (z.D,z.C)
+ z.J,z.K = intersection (C.DC,C.CB)
+\end{tkzelements}
+
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles(A,B C,B D,C)
+\tkzDrawPoints(A,I,C,D,J,K)
+\tkzLabelPoints(A,I,C,D,J,K)
+\end{tikzpicture}
+\end{minipage}
+
+Other examples: \ref{ssub:altshiller}, \ref{sub:the_figure_pappus_circle}
+% subsection circle_circle (end)
+
+\newpage
+\subsection{Line-ellipse} % (fold)
+\label{sub:line_ellipse}
+The following example is complex, but it shows the possibilities of Lua.
+The designation of intersection points is a little more complicated than the previous one, as the argument characterizing the major axis must be taken into account.  The principle is the same, but this argument must be subtracted. In concrete terms, you need to consider the slopes of the lines formed by the center of the ellipse and the points of intersection, and the slope of the major axis.
+
+\begin{minipage}{0.5\textwidth}
+\begin{tkzexample}[code only,small]
+\begin{tkzelements}
+   scale    = .5
+   z.a      = point: new (5 , 2)
+   z.b      = point: new (-4 , 0)
+   z.m      = point: new (2 , 4)
+   z.n      = point: new (4 , 4)
+   L.ab     = line : new (z.a,z.b)
+   L.mn     = line : new (z.m,z.n)
+   z.c      = L.ab. mid
+   z.e      = L.ab: point (-.2)
+   E        = ellipse: foci (z.a,z.b,z.e)
+   z.u,z.v  = intersection (E,L.mn)
+  -- transfer to tex
+   a        = E.Rx
+   b        = E.Ry
+   ang      = math.deg(E.slope)
+   set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[red](a,b u,v) % p,s p,t
+   \tkzDrawPoints(a,b,c,e,u,v) %
+   \tkzLabelPoints(a,b,c,u,v)
+   \tkzDrawEllipse[teal](c,\a,\b,\ang)
+   \tkzDrawSegments(c,u c,v)
+   \tkzFillAngles[green!30,opacity=.4](e,c,v)
+   \tkzFillAngles[green!80,opacity=.4](e,c,u)
+\end{tikzpicture}
+\end{tkzexample}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\begin{tkzelements}
+   scale =.5
+   z.a   = point: new (5 , 2)
+   z.b   = point: new (-4 , 0)
+   z.m   = point: new (2 , 4)
+   z.n   = point: new (4 , 4)
+   L.ab      = line : new (z.a,z.b)
+   L.mn      = line : new (z.m,z.n)
+   z.c   = L.ab. mid
+   z.e   = L.ab: point (-.2)
+   E     = ellipse: foci (z.a,z.b,z.e)
+   z.u,z.v   = intersection (E,L.mn)
+  -- transfer to tex
+   a     = E.Rx
+   b     = E.Ry
+   ang   = math.deg(E.slope)
+   set_lua_to_tex  {'a','b','ang'}
+\end{tkzelements}
+\hspace*{\fill}   
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawLines[red](a,b u,v) % p,s p,t
+   \tkzDrawPoints(a,b,c,e,u,v) %
+   \tkzLabelPoints(a,b,c,u,v)
+   \tkzDrawEllipse[teal](c,\a,\b,\ang)
+   \tkzFillAngles[green!30,opacity=.4](e,c,v)
+   \tkzFillAngles[green!80,opacity=.4](e,c,u)
+   \tkzDrawSegments(c,u c,v)
+\end{tikzpicture}
+\hspace*{\fill}
+\end{minipage}
+
+Other examples: \ref{ssub:function_tkzname_ellipse__foci}, \ref{sub:hexagram}
+%\caption{Intersection line and ellipse}
+
+% \begin{tkzexample}[code only,small]
+% \begin{tkzelements}
+%    scale    = .5
+%    z.a      = point: new (5 , 2)
+%    z.b      = point: new (-4 , 0)
+%    z.m      = point: new (2 , -3)
+%    z.n      = point: new (4 , -3)
+%    L.ab     = line : new (z.a,z.b)
+%    L.mn     = line : new (z.m,z.n)
+%    z.c      = L.ab. mid
+%    z.e      = L.ab: point (-.2)
+%    E        = ellipse: foci (z.a,z.b,z.e)
+%    z.u,z.v  = intersection (E,L.mn)
+%   -- transfer to tex
+%    a        = E.Rx
+%    b        = E.Ry
+%    ang      = math.deg(E.slope)
+%    set_lua_to_tex  {'a','b','ang'}
+% \end{tkzelements}
+%
+% \begin{tikzpicture}
+%    \tkzGetNodes
+%    \tkzDrawLines[red](a,b u,v) % p,s p,t
+%    \tkzDrawPoints(a,b,c,e,u,v) %
+%    \tkzLabelPoints(a,b,c,u,v)
+%    \tkzDrawEllipse[teal](c,\a,\b,\ang)
+%    \tkzDrawSegments(c,u c,v)
+%    \tkzFillAngles[green!30,opacity=.4,size=1.2](e,c,v)
+%    \tkzFillAngles[green!80,opacity=.4](e,c,u)
+% \end{tikzpicture}
+% \end{tkzexample}
+%
+% \begin{tkzelements}
+%    scale=.5
+%    z.a   = point: new (5 , 2)
+%    z.b   = point: new (-4 , 0)
+%    z.m   = point: new (2 , -3)
+%    z.n   = point: new (4 , -3)
+%    L.ab      = line : new (z.a,z.b)
+%    L.mn      = line : new (z.m,z.n)
+%    z.c   = L.ab. mid
+%    z.e   = L.ab: point (-.2)
+%    E     = ellipse: foci (z.a,z.b,z.e)
+%    z.u,z.v   = intersection (E,L.mn)
+%   -- transfer to tex
+%    a     = E.Rx
+%    b     = E.Ry
+%    ang   = math.deg(E.slope)
+%    set_lua_to_tex  {'a','b','ang'}
+% \end{tkzelements}
+%
+%
+% \hspace*{\fill}
+%  \begin{tikzpicture}
+%    \tkzGetNodes
+%    \tkzDrawLines[red](a,b u,v) % p,s p,t
+%    \tkzDrawPoints(a,b,c,e,u,v) %
+%    \tkzLabelPoints(a,b,c,u,v)
+%    \tkzDrawEllipse[teal](c,\a,\b,\ang)
+%    \tkzDrawSegments(c,u c,v)
+%    \tkzFillAngles[green!30,opacity=.4,size=1.2](e,c,v)
+%    \tkzFillAngles[green!80,opacity=.4](e,c,u)
+% \end{tikzpicture}
+% \hspace*{\fill}
+%\caption{Intersection line and ellipse}
+
+% subsection line_ellipse (end)
+% section intersections (end)
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-main.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-main.tex
new file mode 100644
index 00000000000..6fa4bc6166b
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-main.tex
@@ -0,0 +1,198 @@
+% !TEX TS-program = lualatex
+% encoding : utf8 
+% Documentation of tkz-elements v1.00b
+% Copyright 2023  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% This work has the LPPL maintenance status “maintained”.
+% The Current Maintainer of this work is Alain Matthes.
+\PassOptionsToPackage{unicode}{hyperref}
+
+\documentclass[DIV         = 14,
+               fontsize    = 10,
+               index       = totoc,
+               twoside,
+               cadre,
+               headings    = small
+               ]{tkz-doc}
+\gdef\tkznameofpack{tkz-elements}
+\gdef\tkzversionofpack{1.00b}
+\gdef\tkzdateofpack{\today}
+\gdef\tkznameofdoc{tkz-elements.pdf}
+\gdef\tkzversionofdoc{1.00b}
+\gdef\tkzdateofdoc{\today}
+\gdef\tkzauthorofpack{Alain Matthes}
+\gdef\tkzadressofauthor{}
+\gdef\tkznamecollection{AlterMundus}
+\gdef\tkzurlauthor{http://altermundus.fr}
+\gdef\tkzengine{lualatex}
+\gdef\tkzurlauthorcom{http://altermundus.fr}
+\nameoffile{\tkznameofpack}
+% -- Packages ---------------------------------------------------  
+\usepackage[dvipsnames,svgnames]{xcolor}
+\usepackage{calc}
+\usepackage{tkz-base}
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\usepackage{pgfornament}
+\usetikzlibrary{backgrounds}
+\usepackage[colorlinks,pdfencoding=auto, psdextra]{hyperref}
+\hypersetup{
+      linkcolor=Gray,
+      citecolor=Green,
+      filecolor=Mulberry,
+      urlcolor=NavyBlue,
+      menucolor=Gray,
+      runcolor=Mulberry,
+      linkbordercolor=Gray,
+      citebordercolor=Green,
+      filebordercolor=Mulberry,
+      urlbordercolor=NavyBlue,
+      menubordercolor=Gray,
+      runbordercolor=Mulberry,
+      pdfsubject={Euclidean Geometry},
+      pdfauthor={\tkzauthorofpack},
+      pdftitle={\tkznameofpack},
+      pdfcreator={\tkzengine}
+}
+\usepackage{tkzexample}
+\usepackage{fontspec}
+\setmainfont{texgyrepagella}[
+  Extension = .otf,
+  UprightFont = *-regular ,
+  ItalicFont  = *-italic  ,
+  BoldFont    = *-bold    ,
+  BoldItalicFont = *-bolditalic
+]
+\setsansfont{texgyreheros}[
+  Extension = .otf,
+  UprightFont = *-regular ,
+  ItalicFont  = *-italic  ,
+  BoldFont    = *-bold    ,
+  BoldItalicFont = *-bolditalic ,
+]
+
+\setmonofont{lmmono10-regular.otf}[
+  Numbers={Lining,SlashedZero},
+  ItalicFont=lmmonoslant10-regular.otf,
+  BoldFont=lmmonolt10-bold.otf,
+  BoldItalicFont=lmmonolt10-boldoblique.otf,
+]
+\newfontfamily\ttcondensed{lmmonoltcond10-regular.otf}
+%% (La)TeX font-related declarations:
+\linespread{1.05}  % Pagella needs more space between lines
+\usepackage[math-style=literal,bold-style=literal]{unicode-math}
+\usepackage{fourier-otf}
+\let\rmfamily\ttfamily
+\usepackage{multicol,lscape}
+\usepackage[english]{babel}
+\usepackage[normalem]{ulem}
+\usepackage{multirow,multido,booktabs,cellspace}
+\usepackage{shortvrb,fancyvrb,bookmark} 
+\usepackage{makeidx}
+%\usepackage{float}
+\makeindex 
+
+\makeatletter
+\renewenvironment{theindex}
+   {\section*{\indexname}\begin{multicols}{2}%
+    \@mkboth{\MakeUppercase\indexname}%
+  {\MakeUppercase\indexname}%
+    \thispagestyle{plain}\parindent\z@
+    \parskip\z@ \@plus .3\p@\relax
+    \columnseprule \z@
+    \columnsep 35\p@
+    \let\item\@idxitem}
+   {\end{multicols}}
+\makeatother
+\newcommand*{\tkzfname}[1]{\Amacro{#1}\textbf{\texttt{\textcolor{MidnightBlue}{%
+ #1}}}}
+ \newcommand*{\tkzmname}[1]{\Amacro{#1}\textbf{\texttt{\textcolor{MidnightBlue}{%
+#1}}}}
+ \newcommand*{\tkzaname}[1]{\Amacro{#1}\textbf{\texttt{\textcolor{MidnightBlue}{%
+#1}}}}  
+\def\langle{} \def\rangle{}
+\renewcommand*{\IargName}[2]{\texttt{#2}\index{#1_2@\texttt{#1: argument(s)}!\texttt{#2}}}
+\newcommand*{\Amacro}[1]{\index{#1_1@\texttt{#1}}}
+\renewcommand*{\IoptName}[2]{\texttt{#2}\index{#1_3@\texttt{#1: attribute(s)}!\texttt{#2}}}
+\newcommand*{\Iattr}[2]{\texttt{#2}\index{#1_3@\texttt{#1:  attribute}!\texttt{#2}}}
+\newcommand*{\Imeth}[2]{\texttt{#2}\index{#1_3@\texttt{#1:  method}!\texttt{#2}}}
+\newcommand*{\Igfct}[2]{\texttt{#2}\index{#1_3@\texttt{#1:  function}!\texttt{#2}}}
+\newcommand*{\Iclass}[2]{\texttt{#2}\index{#1_3@\texttt{#1:  class}!\texttt{#2}}}
+\newcommand*{\tkzNameObj}[1]{\tkzname{#1}\Iobj{#1}}
+\newcommand*{\Iobj}[1]{\index{Object_1@\texttt{Object}!\texttt{#1}}}
+
+%<---------------------------------------------------------------------------> 
+% settings styles
+\tkzSetUpColors[background=white,text=black]  
+\tkzSetUpCompass[color=orange, line width=.2pt,delta=10]
+\tkzSetUpArc[color=gray,line width=.2pt]
+\tkzSetUpPoint[size=2,color=teal]
+\tkzSetUpLine[line width=.2pt,color=teal]
+\tkzSetUpStyle[color=orange,line width=.2pt]{new}
+\tikzset{every picture/.style={line width=.2pt}}
+\tikzset{label angle style/.append style={color=teal,font=\footnotesize}} 
+\tikzset{label style/.append style={below,color=teal,font=\scriptsize}}
+\tikzset{new/.style={color=orange,line width=.2pt}} 
+\def\tkzar{\hspace{1em}-->\hspace{1em}}
+
+\AtBeginDocument{\MakeShortVerb{\|}} % link to shortvrb
+\begin{document} 
+  
+\parindent=0pt
+\tkzTitleFrame{tkz-elements \tkzversionofpack\\Euclidean Geometry}
+\clearpage
+
+\defoffile{\lefthand\
+ This document brings together some notes about  \tkzname{\tkznameofpack}, the first version of a library written in lua, allowing to make all the necessary calculations to define the objects of a Euclidean geometry figure. You need to compile with Lua\LaTeX.\\ With \pkg{tkz-elements}, the definitions and calculations are only done with \pkg{lua}. \\ The main possibility of programmation  proposed is oriented "object programming" with object classes like point, line, triangle, circle and ellipse.  For the moment, once the calculations are done, it is \pkg{tkz-euclide} or   \pkg{TikZ} which allows the drawings.\\
+ I discovered Lua and object-oriented programming when I created this package, so it's highly probable that I've made a few mistakes.  If you'd like to participate in the development of this package or give me advice on how to proceed, please contact me via my email. \\ This version \tkzversionofpack\ is a beta version.\\
+English is  not my native language so there  might be some errors.
+}
+
+\presentation
+
+\vspace*{1cm}
+
+\lefthand\ Acknowledgements : I received much valuable advice, remarks, corrections  from \\ \tkzimp{Nicolas Kisselhoff}, \tkzimp{David Carlisle}, \tkzimp{Roberto Giacomelli} and \tkzimp{Qrrbrbirlbel}.
+
+\vspace*{12pt}
+\lefthand\ I would also like to thank \tkzimp{Eric Weisstein}, creator of 
+\href{http://mathworld.wolfram.com/about/author.html}{MathWorld}.
+
+\vspace*{12pt}
+\lefthand\ You can find some examples on my site:
+\href{http://altermundus.fr}{altermundus.fr}. \hspace{2cm} under construction!
+
+\vfill
+Please report typos or any other comments to this documentation to: \href{mailto:al.ma@mac.com}{\textcolor{blue}{Alain Matthes}}.
+
+This file can be redistributed and/or modified under the terms of the \LaTeX{} 
+Project Public License Distributed from \href{http://www.ctan.org/}{CTAN}\  archives.
+
+\clearpage
+\tableofcontents
+
+\clearpage
+\newpage
+
+\input{TKZdoc-elements-presentation.tex}
+\input{TKZdoc-elements-convention.tex}
+\input{TKZdoc-elements-howtouse.tex}
+\input{TKZdoc-elements-classes.tex}
+\input{TKZdoc-elements-classes-point.tex}
+\input{TKZdoc-elements-classes-line.tex}
+\input{TKZdoc-elements-classes-circle.tex}
+\input{TKZdoc-elements-classes-triangle.tex}
+\input{TKZdoc-elements-classes-ellipse.tex}
+\input{TKZdoc-elements-classes-misc.tex}
+\input{TKZdoc-elements-intersection.tex}
+\input{TKZdoc-elements-examples.tex}
+
+\clearpage\newpage
+\small\printindex
+\end{document}
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-presentation.tex b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-presentation.tex
new file mode 100644
index 00000000000..d837d4a8263
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-presentation.tex
@@ -0,0 +1,167 @@
+\section{Presentation}
+
+I created \pkg{tkz-euclide} to give math teachers and students a tool to draw Euclidean geometry figures. This package was created as an interface based on \pkg{TikZ}, itself based on \TEX{}. The only problem encountered with this method is, in complicated cases, the lack of precision of the calculations made by \TEX{}.
+
+To remedy this lack of precision, I first introduced the package \pkg{fp}, then the package \pkg{xfp}. Lately, with the arrival of lua\LATEX{}, I have been able to add a \tkzname{Lua} option whose goal was to perform some calculations with \tkzname{Lua}. It is much easier to program mathematics with \tkzname{Lua} than with \TEX{} so having prepared \pkg{tkz-euclide}, by separating the first parts of definitions and calculations from the drawing part, the idea of carrying out the first parts with only \tkzname{Lua} was necessary.
+
+I had received some examples of programming with \tkzname{Lua} from Nicolas Kisselhoff and I took many of his ideas.
+
+The essential principles of figure construction with \tkzname{tkz-euclide} are kept: definition, calculations, tracings, labels as well as the  step-by-step programmation, corresponding to a construction with a ruler and a compass.
+
+Then, I read an article by Roberto Giacomelli on object programming based on the \tkzname{Lua} and \TIKZ\ tools. This was my second source of inspiration. Not only could the programming be done step-by-step, but the introduction of objects allowed the link between the code and the geometry. The code becomes more readable, the code is more explicit and better structured but it is less concise. Finally, as the problem of precision disappeared, I came to appreciate more and more what I was getting with object programming. So I've tried to develop this programming as much as possible.
+
+In order to organize and maintain all the functions and methods, I chose to use classes of objects whose main ones are \tkzname{point}, \tkzname{line}, \tkzname{triangle}, \tkzname{circle} and \tkzname{ellipse}.
+
+\subsection{With Lua} % (fold)
+\label{sub:with_lua}
+
+The purpose of tkz-elements is simply to calculate dimensions and define points. This is done in Lua. You can think of tkz-elements as a kernel that will be used either by tkz-euclide or by TikZ, see MetaPost.
+Definitions and calculations are done inside the environment \tkzNameEnv{tkzelements}, this environment is based on \tkzNameEnv{luacode}.
+To improve precision, if it's necessary to modify the scale of your figure, it's best to change the "scale" variable at the start of the code placed in environment \tkzNameEnv{tkzelements}.
+Then we need to be able to transfer the coordinates of the points to a package that can use them, in this case tkz-euclide or TikZ.
+% subsection with_lua (end)
+
+\subsection{The main process : from tkz-elements (lua) to tkz-euclide (TikZ) with Lua\LaTeX.} % (fold)
+\label{sub:the_main_process}
+
+
+When all the points necessary for the drawing are obtained, they must be transformed into \tkzname{nodes} so that \pkg{TikZ} or \pkg{tkz-euclide} can draw the figure. This is done through the macro \tkzcname{tkzGetNodes}. This macro browse all the elements of the table |z| using the key (in fact the name of the point) and retrieves the values associated with it, i.e. the coordinates of the point (node).
+
+A point $A$ is defined and stored in tkz-elements as follows:
+|z.A| is an element of a table |z| which contains the coordinates of $A$ in the form of a complex number (very useful for calculations). Then a  macro, \tkzcname{tkzGetNodes}, transforms all elements of table |z| into nodes usable by tkz-euclide or TikZ. For another package, you'll need to adapt \tkzcname{tkzGetNodes}.
+
+% subsection the_main_process (end)
+
+\newpage
+\subsection{Complete example: Pappus circle} % (fold)
+\label{sub:the_figure_pappus_circle}
+
+The figure:
+
+\begin{tkzelements}
+  z.A  = point: new (0 , 0)
+  z.B  = point: new (10 , 0)
+  L.AB = line:  new ( z.A, z.B)
+  z.C  = L.AB:  gold_ratio () 
+  L.AC = line:  new ( z.A, z.C)
+  L.CB = line:  new ( z.C, z.B)
+  L.AB = line:  new ( z.A, z.B)
+  z.O_0    = L.AB.mid
+  z.O_1    = L.AC.mid
+  z.O_2    = L.CB.mid
+  C.AB = circle: new ( z.O_0, z.B) 
+  C.AC = circle: new ( z.O_1, z.C) 
+  C.CB = circle: new ( z.O_2, z.B)
+  z.P  = C.CB.north  
+  z.Q  = C.AC.north
+  z.O  = C.AB.south
+  z.c  = z.C : north (2)
+  C.PC = circle: new ( z.P, z.C) 
+  C.QA = circle: new ( z.Q, z.A)  
+  z.P_0    = intersection (C.PC,C.AB)
+  z.P_1    = intersection (C.PC,C.AC)
+  _,z.P_2  = intersection (C.QA,C.CB)
+ T     = triangle: new ( z.P_0, z.P_1, z.P_2)
+ z.O_3 = T.circumcenter
+\end{tkzelements}
+\hspace*{\fill}
+   \begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawCircle[black,fill=yellow!20,opacity=.4](O_0,B)
+  \tkzDrawCircles[teal,fill=teal!40,opacity=.6](O_1,C O_2,B)
+  \tkzDrawCircle[purple,fill=purple!20,opacity=.4](O_3,P_0)
+  \tkzDrawArc[cyan,delta=10](Q,A)(P_0)
+  \tkzDrawArc[cyan,delta=10](P,P_0)(B)
+  \tkzDrawArc[cyan,delta=10](O,B)(A)
+  \tkzDrawPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+  \tkzLabelPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+   \end{tikzpicture}
+\hspace*{\fill}
+% subsection the_figure_pappus_circle (end)
+
+\subsubsection{The code} % (fold)
+\label{ssub:the_code}
+
+\begin{tkzexample}[small, code only,num]
+% !TEX TS-program = lualatex
+\documentclass{article}
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document}
+
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (10 , 0)
+   L.AB     = line:  new ( z.A, z.B)
+   z.C      = L.AB:  gold_ratio () 
+   L.AC     = line:  new ( z.A, z.C)
+   L.CB     = line:  new ( z.C, z.B)
+   L.AB     = line:  new ( z.A, z.B)
+   z.O_0    = L.AB.mid
+   z.O_1    = L.AC.mid
+   z.O_2    = L.CB.mid
+   C.AB     = circle: new ( z.O_0, z.B) 
+   C.AC     = circle: new ( z.O_1, z.C) 
+   C.CB     = circle: new ( z.O_2, z.B)
+   z.P      = C.CB.north  
+   z.Q      = C.AC.north
+   z.O      = C.AB.south
+   z.c      = z.C : north (2)
+   C.PC     = circle: new ( z.P, z.C) 
+   C.QA     = circle: new ( z.Q, z.A)  
+   z.P_0    = intersection (C.PC,C.AB)
+   z.P_1    = intersection (C.PC,C.AC)
+   _,z.P_2  = intersection (C.QA,C.CB)
+   T        = triangle: new ( z.P_0, z.P_1, z.P_2)
+   z.O_3    = T.circumcenter
+\end{tkzelements}
+
+\begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawCircle[black,fill=yellow!20,opacity=.4](O_0,B)
+  \tkzDrawCircles[teal,fill=teal!40,opacity=.6](O_1,C O_2,B)
+  \tkzDrawCircle[purple,fill=purple!20,opacity=.4](O_3,P_0)
+  \tkzDrawArc[cyan,delta=10](Q,A)(P_0)
+  \tkzDrawArc[cyan,delta=10](P,P_0)(B)
+  \tkzDrawArc[cyan,delta=10](O,B)(A)
+  \tkzDrawPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+  \tkzLabelPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+\end{tikzpicture}
+\end{document}
+\end{tkzexample}
+% subsubsection the_code (end)
+
+\subsubsection{Some explanations} % (fold)
+\label{ssub:some_explanations}
+
+Half of the code concerns the direct creation of objects (|point: new |, |circle: new | etc.)
+
+Then points are obtained using object attributes like |L.AB.mid| which determines the middle of the segment $[AB]$ or |C.AB.south| which allows to obtain the south pole of the circle with center $A$ passing through $B$.
+
+About the naming of objects, see the section \ref{sec:writing_convention}
+
+\begin{itemize}
+  \item  Lines 8 and 9 create two fixed points $A$ and $B$.
+
+ \item   Line 10 these two points are used to create the line.
+
+ \item   Line 11 the gold method creates a point $C$ which divides the segment $[AB]$ according to the golden ratio.  
+
+ \item  Lines 12, 13 and 14 creation of 3 new lines.
+
+\item    Lines 15, 16 and 17 creation of 3 points: the midpoints of the previous segments. These points are predefined and it is enough to use the attributes of the lines. Another possibility is to use the triangle T.ABC with the method : |medial_tr|
+
+\item    Lines 18, 19 et 20 creation of three circles.
+
+\item    Line 21 creation of the south pole $P$ of the circle of center C passing through B. It is also a predefined point and we still use an attribute.
+
+\item   Lines 22 and 23 we create two new poles: north and south for two other circles.
+
+\item    Lines 24 and 25 creation of two circles.
+
+\item    Lines 26 and 27 search for intersections of two circles.
+
+\item    Lines 28 and 29 we use a triangle to search for its circum center.
+\end{itemize}
+% subsubsection some_explanations (end)
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo-1.pdf b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo-1.pdf
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diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_1.pdf b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_1.pdf
new file mode 100644
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diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_1.tex b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_1.tex
new file mode 100644
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@@ -0,0 +1,46 @@
+% !TEX TS-program = lualatex
+% Author Alain Matthes 2023
+\documentclass{article}
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document}
+
+\begin{tkzelements}
+   z.A      = point: new (0 , 0)
+   z.B      = point: new (10 , 0)
+   L.AB     = line:  new ( z.A, z.B)
+   z.C      = L.AB:  gold_ratio () 
+   L.AC     = line:  new ( z.A, z.C)
+   L.CB     = line:  new ( z.C, z.B)
+   L.AB     = line:  new ( z.A, z.B)
+   z.O_0    = L.AB.mid
+   z.O_1    = L.AC.mid
+   z.O_2    = L.CB.mid
+   C.AB     = circle: new ( z.O_0, z.B) 
+   C.AC     = circle: new ( z.O_1, z.C) 
+   C.CB     = circle: new ( z.O_2, z.B)
+   z.P      = C.CB.north  
+   z.Q      = C.AC.north
+   z.O      = C.AB.south
+   z.c      = z.C : north (2)
+   C.PC     = circle: new ( z.P, z.C) 
+   C.QA     = circle: new ( z.Q, z.A)  
+   z.P_0    = intersection (C.PC,C.AB)
+   z.P_1    = intersection (C.PC,C.AC)
+   _,z.P_2  = intersection (C.QA,C.CB)
+   T        = triangle: new ( z.P_0, z.P_1, z.P_2)
+   z.O_3    = T.circumcenter
+\end{tkzelements}
+
+\begin{tikzpicture}
+  \tkzGetNodes
+  \tkzDrawCircle[black,fill=yellow!20,opacity=.4](O_0,B)
+  \tkzDrawCircles[teal,fill=teal!40,opacity=.6](O_1,C O_2,B)
+  \tkzDrawCircle[purple,fill=purple!20,opacity=.4](O_3,P_0)
+  \tkzDrawArc[cyan,delta=10](Q,A)(P_0)
+  \tkzDrawArc[cyan,delta=10](P,P_0)(B)
+  \tkzDrawArc[cyan,delta=10](O,B)(A)
+  \tkzDrawPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+  \tkzLabelPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O)
+\end{tikzpicture}
+\end{document}
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_2.pdf b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_2.pdf
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diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_2.tex b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_2.tex
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+++ b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_2.tex
@@ -0,0 +1,59 @@
+% !TEX TS-program = lualatex
+% Author Alain Matthes 2023
+\documentclass{article} 
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document} 
+
+ The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles    
+
+\begin{tkzelements}
+      scale    =  .5
+      z.A                  = point: new (0,0)
+      z.B                  = point: new (6,0)
+      z.C                  = point: new (0.8,4)
+      T.ABC                = triangle : new (z.A,z.B,z.C) 
+      C.euler              = T.ABC: euler_circle ()
+      z.N,z.Ma             = get_points (C.euler)      
+      z.I_a,z.I_b,z.I_c    = get_points (T.ABC : excentral())
+      z.Ea,z.Eb,z.Ec       = get_points (T.ABC : feuerbach ())
+      z.S,z.p              = get_points (T.ABC : spieker_circle ())
+      -- S spieker point is the radical center of the last three circles
+      C.exa                = T.ABC : ex_circle ()
+      C.exb                = T.ABC : ex_circle (1)
+      C.exc                = T.ABC : ex_circle (2)      
+      _,z.Xa               = get_points (C.exa)
+      _,z.Xb               = get_points (C.exb)
+      _,z.Xc               = get_points (C.exc) 
+      L.fa                 = line : new (z.S,z.Ea) 
+      L.fb                 = line : new (z.S,z.Eb)
+      L.fc                 = line : new (z.S,z.Ec)
+      z.f_a                = intersection (L.fa,C.exa)
+      z.f_b                = intersection (L.fb,C.exb)
+      _,z.f_c              = intersection (L.fc,C.exc)
+      T                    = triangle : new ( z.f_a, z.f_b , z.f_c )
+      z.o                  = T.circumcenter
+      _,z.l                = get_points (C.exa : orthogonal_from (z.S))
+      -- S center of inversion !!
+\end{tkzelements}
+\vspace*{2em}
+\hfill
+\begin{tikzpicture}
+\tkzSetUpLine[ultra thin,color=teal]
+\tkzGetNodes
+\tkzDrawCircles[red](o,f_a  N,Ma)
+\tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
+\tkzClipCircle(o,f_a)
+\tkzDrawLines[add=3 and 3](A,B A,C B,C)
+\tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
+\tkzDrawCircles[cyan](S,l)
+\tkzDrawPoints(A,B,C)
+\tkzDrawPoints[cyan](S)
+\tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
+\tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
+\end{tikzpicture}
+\hfill
+\end{document}
+
+
+           
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.pdf b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.pdf
new file mode 100644
index 00000000000..1873fd5c853
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.pdf
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.tex b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.tex
new file mode 100644
index 00000000000..684475e28e4
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/examples/tkz-elements-demo_3.tex
@@ -0,0 +1,62 @@
+% !TEX TS-program = lualatex
+% Author Alain Matthes 2023
+\documentclass{article}
+\usepackage{tkz-euclide}
+\usepackage{tkz-elements}
+\begin{document}
+
+\begin{tkzelements}
+   scale = 2
+   z.A                  = point: new (0 , 0)
+   z.B                  = point: new (5 , 1)
+   L.AB                 = line : new (z.A,z.B)
+   z.C                  = point: new (.8 , 3)
+   T.ABC                = triangle: new (z.A,z.B,z.C)
+   z.N                  = T.ABC.eulercenter
+   z.G                  = T.ABC.centroid
+   z.O                  = T.ABC.circumcenter
+   z.H                  = T.ABC.orthocenter
+   z.Ma,z.Mb,z.Mc       = get_points (T.ABC : medial ())
+   z.Ha,z.Hb,z.Hc       = get_points (T.ABC : orthic ())   
+   z.Ea,z.Eb,z.Ec       = get_points (T.ABC: extouch())
+   L.euler              = T.ABC : euler_line () 
+   C.circum             = T.ABC : circum_circle () 
+   C.euler              = T.ABC : euler_circle () 
+   z.I,z.J              = intersection (L.euler,C.euler) 
+   E                    = ellipse: foci (z.H,z.O,z.I)  
+   a                    = E.Rx
+   b                    = E.Ry
+   ang                  = math.deg(E.slope)
+   L.AH                 = line: new (z.A,z.H)
+   L.BH                 = line: new (z.B,z.H)
+   L.CH                 = line: new (z.C,z.H)
+   z.X                  = intersection (L.AH,C.circum)  
+   _,z.Y                = intersection (L.BH,C.circum)  
+   _,z.Z                = intersection (L.CH,C.circum)  
+   L.BC                 = line: new (z.B,z.C) 
+   L.XO                 = line: new (z.X,z.O)
+   L.YO                 = line: new (z.Y,z.O)
+   L.ZO                 = line: new (z.Z,z.O)
+   z.x                  = intersection (L.BC,L.XO)
+   z.U                  = intersection (L.XO,E)
+   _,z.V                = intersection (L.YO,E)
+   _,z.W                = intersection (L.ZO,E)
+    set_lua_to_tex {'a','b','ang'} 
+ \end{tkzelements}
+
+\begin{tikzpicture}
+   \tkzGetNodes
+   \tkzDrawPolygon(A,B,C)
+   \tkzDrawCircles[red](N,Ma O,A)
+   \tkzDrawSegments(A,X B,Y C,Z B,Hb C,Hc X,O Y,O Z,O)
+   \tkzDrawPolygon[red](U,V,W)
+   \tkzLabelPoints[red](U,V,W)
+   \tkzLabelPoints(A,B,C,X,Y,Z)
+   \tkzDrawLine[blue](I,J)
+   \tkzLabelPoints[blue,right](O,N,G,H,I,J)
+   \tkzDrawPoints(I,J,U,V,W)
+   \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
+   \tkzDrawEllipse[blue](N,\a,\b,\ang)
+\end{tikzpicture}
+\end{document}
+
diff --git a/Master/texmf-dist/doc/latex/tkz-elements/tkz-elements.pdf b/Master/texmf-dist/doc/latex/tkz-elements/tkz-elements.pdf
new file mode 100644
index 00000000000..7c2839b3f4a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/tkz-elements/tkz-elements.pdf