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-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex480
1 files changed, 251 insertions, 229 deletions
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
index 9e79877299..5efb52381f 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
@@ -179,22 +179,23 @@ z.E = intersection (L.AI,L.LLC)
\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)
+ 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
+ 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)
+ 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)
@@ -210,26 +211,24 @@ scale=.75
\tkzMarkAngles[mark=|](A,M,C C,M,B)
\tkzMarkAngles[mark=||](B,M,D D,M,E)
\end{tikzpicture}
-\end{tkzexample}
-
+\hspace*{\fill}
+\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)
+ 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
+ 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)
+ 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)
@@ -245,7 +244,12 @@ scale=.75
\tkzMarkAngles[mark=|](A,M,C C,M,B)
\tkzMarkAngles[mark=||](B,M,D D,M,E)
\end{tikzpicture}
-\hspace*{\fill}
+\end{tkzexample}
+
+Remark : The circle can be obtained with:
+
+|C.AB = T.MAB.bc : apollonius (length(z.M,z.A)/length(z.M,z.B))|
+
%subsection apollonius_circle (end)
@@ -428,8 +432,8 @@ Same result using the function |T.ABC.ab : apollonius (k) |
z.w1,z.t1 = get_points ( C.AB )
C.AC = T.ABC.ca : apollonius (length(z.B,z.C)/length(z.B,z.A))
z.w2,z.t2 = get_points ( C.AC )
- C.AC = T.ABC.bc : apollonius (length(z.A,z.B)/length(z.A,z.C))
- z.w3,z.t3 = get_points ( C.AC )
+ C.BC = T.ABC.bc : apollonius (length(z.A,z.B)/length(z.A,z.C))
+ z.w3,z.t3 = get_points ( C.BC )
\end{tkzelements}
\end{verbatim}
@@ -733,19 +737,19 @@ Same result using the function |T.ABC.ab : apollonius (k) |
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}
+\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}
% subsection orthogonal_circle_through (end)
-\subsection{Devine ratio} % (fold)
-\label{sub:devine_ratio}
+\subsection{Divine ratio} % (fold)
+\label{sub:divine_ratio}
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
@@ -809,52 +813,53 @@ 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}
-% subsection devine_ratio (end)
+\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}
+% subsection divine_ratio (end)
\subsection{Director circle} % (fold)
\label{sub:director_circle}
% modif C: point (0.25) instead of 2
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
- \begin{verbatim}
- \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 (0.25)
- L.J,L.K = E: tangent_from (z.L)
- z.J = L.J.pb
- z.K = L.K.pb
- \end{tkzelements}
- \begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawPoints(F1,F2,O)
- \tkzDrawCircles[teal](O,P)
- \tkzDrawPolygon(H,O,A,P)
- \tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{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{verbatim}
+\begin{verbatim}
+\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 (0.25)
+ L.J,L.K = E: tangent_from (z.L)
+ z.J = L.J.pb
+ z.K = L.K.pb
+\end{tkzelements}
+\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPoints(F1,F2,O)
+ \tkzDrawCircles[teal](O,P)
+ \tkzDrawPolygon(H,O,A,P)
+ \tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{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)
+ \tkzLabelPoints[above](L)
+ \tkzMarkRightAngles(A,P,H J,L,K)
+\end{tikzpicture}
+\end{verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -885,6 +890,7 @@ z.K = L.K.pb
\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)
+\tkzLabelPoints[above](L)
\tkzMarkRightAngles(A,P,H J,L,K)
\end{tikzpicture}
\end{minipage}
@@ -942,8 +948,8 @@ z.C = intersection (L.EG,L.AB)
z.O = C.AB: antipode (z.B)
\end{tkzelements}
- \hspace*{\fill}
- \begin{tikzpicture}
+\hspace*{\fill}
+\begin{tikzpicture}
\tkzGetNodes
\tkzDrawArc[delta=5](O,B)(G)
\tkzDrawCircles(A,B B,A)
@@ -952,13 +958,13 @@ z.O = C.AB: antipode (z.B)
\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}
+\end{tikzpicture}
+ \hspace*{\fill}
% subsection gold_division (end)
\subsection{Ellipse} % (fold)
\label{sub:ellipse}
-
+\begin{minipage}{.5\textwidth}
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
z.C = point: new (3 , 2)
@@ -971,7 +977,6 @@ z.O = C.AB: antipode (z.B)
a = E.Rx
b = E.Ry
slope = math.deg(E.slope)
-
\end{tkzelements}
\begin{tikzpicture}
\tkzGetNodes
@@ -981,7 +986,8 @@ z.O = C.AB: antipode (z.B)
\tkzLabelPoints(C,A,B)
\end{tikzpicture}
\end{tkzexample}
-
+\end{minipage}
+\begin{minipage}{.5\textwidth}
\begin{tkzelements}
z.C = point: new (3 , 2)
z.A = point: new (5 , 1)
@@ -1004,53 +1010,55 @@ slope = math.deg(E.slope)
\tkzLabelPoints(C,A,B)
\end{tikzpicture}
\hspace*{\fill}
+\end{minipage}
% subsection ellipse (end)
\subsection{Ellipse with radii} % (fold)
\label{sub:ellipse_with_radii}
-
+\begin{minipage}{.5\textwidth}
\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 (0.25)
-\end{tkzelements}
-\begin{tikzpicture}
+scale=.5
+z.C = point: new (0 , 4)
+b = value(math.sqrt(8))
+a = value(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)
+\end{tkzelements}
+\begin{tikzpicture}[gridded]
\tkzGetNodes
-\tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
+\tkzDrawEllipse[blue](C,\tkzUseLua{a},
+ \tkzUseLua{b},\tkzUseLua{ang})
\tkzDrawPoints(C,V,CoV)
\end{tikzpicture}
\end{tkzexample}
-
+\end{minipage}
+\begin{minipage}{.5\textwidth}
\begin{tkzelements}
+scale=.5
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)
+b = value(math.sqrt(8))
+a = value(math.sqrt(32))
ang = math.deg(math.pi/4)
-E = ellipse: radii (z.C,a,b,math.pi/4)
+E = ellipse: radii (z.C,a,b,math.pi/4)
z.V = E : point (0)
-z.CoV = E : point (0.25)
-\end{tkzelements}
+z.CoV = E : point (math.pi/2)
+\end{tkzelements}
\hspace*{\fill}
-\begin{tikzpicture}
+\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
\tkzDrawPoints(C,V,CoV)
\end{tikzpicture}
+\end{minipage}
% subsection ellipse_with_radii (end)
\subsection{Ellipse\_with\_foci} % (fold)
\label{sub:ellipse_with_foci}
-
+\begin{minipage}{.5\textwidth}
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
local e
@@ -1079,7 +1087,8 @@ z.CoV = E : point (0.25)
\tkzDrawLines(K,F K,G)
\end{tikzpicture}
\end{tkzexample}
-
+\end{minipage}
+\begin{minipage}{.5\textwidth}
\begin{tkzelements}
local e
e = .8
@@ -1109,27 +1118,28 @@ z.G = L.tb.pb
\tkzDrawLines(K,F K,G)
\end{tikzpicture}
\hspace*{\fill}
+ \end{minipage}
% subsection ellipse_with_foci (end)
\subsection{Euler relation} % (fold)
\label{sub:euler_relation}
-
+\begin{minipage}{.5\textwidth}
\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)
+ 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
@@ -1143,7 +1153,8 @@ z.G = L.tb.pb
\tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J)
\end{tikzpicture}
\end{tkzexample}
-
+\end{minipage}
+\begin{minipage}{.5\textwidth}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (5 , 0)
@@ -1173,6 +1184,7 @@ _,z.E = intersection (L.Ow, C.OA)
\tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J)
\end{tikzpicture}
\hspace*{\fill}
+\end{minipage}
% subsection euler_relation (end)
\subsection{External angle} % (fold)
@@ -1180,33 +1192,33 @@ _,z.E = intersection (L.Ow, C.OA)
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{verbatim}
\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)
+ scale = .75
+ 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)
+ \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{verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
-scale = .8
+scale = .75
z.A = point: new (0 , 0)
z.B = point: new (5 , 0)
z.C = point: new (-2 , 4)
@@ -1230,6 +1242,7 @@ z.E = z.C: symmetry (z.B)
\tkzLabelPoints[above](C)
\tkzLabelPoints(A,B,D)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection external_angle (end)
@@ -1488,7 +1501,7 @@ z.O_0 = L.AB.mid
\subsection{Harmonic division v1} % (fold)
\label{sub:harmonic_division_v1}
-\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
+\begin{minipage}[t]{.4\textwidth}\vspace{0pt}%
\begin{verbatim}
\begin{tkzelements}
scale=.75
@@ -1523,7 +1536,7 @@ z.C = intersection (L.XG,L.AB)
\end{tikzpicture}
\end{verbatim}
\end{minipage}
-\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
+\begin{minipage}[t]{.6\textwidth}\vspace{0pt}%
\begin{tkzelements}
scale=.75
z.A = point: new (0 , 0)
@@ -1556,6 +1569,7 @@ z.C = intersection (L.XG,L.AB)
\tkzLabelPoints(A,B,G,E,F,C,D)
\tkzMarkSegments(F,B B,E)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection harmonic_division_v1 (end)
@@ -1621,7 +1635,7 @@ z.C = intersection (L.GX,L.AB)
\subsection{Menelaus} % (fold)
\label{sub:menelaus}
-\begin{minipage}{.5\textwidth}
+\begin{minipage}{.4\textwidth}
\begin{verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
@@ -1645,7 +1659,7 @@ z.C = intersection (L.GX,L.AB)
\end{tikzpicture}
\end{verbatim}
\end{minipage}
-\begin{minipage}{.5\textwidth}
+\begin{minipage}{.6\textwidth}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (6 , 0)
@@ -1668,6 +1682,7 @@ z.R = intersection (L.BC,L.PX)
\tkzDrawPoints(P,Q,R,A,B,C)
\tkzLabelPoints(A,B,C,P,Q,R)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection menelaus (end)
@@ -2041,7 +2056,7 @@ z.H = L.OOp : projection (z.X)
\end{minipage}
% subsection radical_circle (end)
-\subsection{Hexagram} % (fold)
+\subsection{Euler ellipse} % (fold)
\label{sub:hexagram}
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
@@ -2080,6 +2095,9 @@ z.H = L.OOp : projection (z.X)
_,z.V = intersection (L.YO,E)
_,z.W = intersection (L.ZO,E)
\end{tkzelements}
+ \end{tkzexample}
+
+\begin{tkzexample}[latex=0cm,small,code only]
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPolygon(A,B,C)
@@ -2419,7 +2437,7 @@ z.O = C.DC : inversion (z.W)
\end{tkzexample}
\begin{tkzelements}
-scale =.3
+scale =.5
z.A = point: new (0,0)
z.B = point: new (6,0)
z.C = point: new (0.8,4)
@@ -2665,6 +2683,84 @@ z.Kp = L.Kp.pb
\subsection{Midcircles} % (fold)
\label{sub:midcircles}
+\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 : 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}
+
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
z.A = point: new (0 , 0)
@@ -2712,7 +2808,9 @@ z.Kp = L.Kp.pb
z.Ap = z.M_1: symmetry (z.A)
z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
\end{tkzelements}
+\end{tkzexample}
+\begin{tkzexample}[latex=0cm,small,code only]
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle[thin,fill=green!10](O_4,P_0)
@@ -2743,83 +2841,7 @@ z.Kp = L.Kp.pb
\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 : 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}
% subsection midcircles (end)
\subsection{Pencil v1} % (fold)
@@ -4452,11 +4474,11 @@ z.L = T.golden.pc
L.O0L = line:new(z.O_0,z.L)
z.D = intersection (L.O0L,C.O0B)
L.DB = line:new(z.D,z.B)
-z.Z = intersection (L.DB,C.O2B)
+_,z.Z = intersection (L.DB,C.O2B)
L.DA = line:new(z.D,z.A)
z.I = intersection (L.DA,C.O1C)
L.O2Z = line:new(z.O_2,z.Z)
-z.H = intersection (L.O2Z,C.O0B)
+_,z.H = intersection (L.O2Z,C.O0B)
C.BD = circle:new (z.B,z.D)
C.DB = circle:new (z.D,z.B)
_,z.G = intersection (C.BD,C.O0B)