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-rw-r--r--Master/texmf-dist/doc/latex/tkz-elements/TKZdoc-elements-classes-circle.tex375
1 files changed, 218 insertions, 157 deletions
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
index 85e73595189..2d5665f879b 100644
--- 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
@@ -38,7 +38,8 @@ Three attributes are used (south, west, radius).
\begin{minipage}{0.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .5
z.a = point: new (1, 1)
z.b = point: new (5, 4)
@@ -48,7 +49,7 @@ Three attributes are used (south, west, radius).
r = C.ab.radius
z.c = C.ab.opp
z.r,z.t = get_points (C.ab.ct : ortho_from (z.b))
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPoints(a,b,c,s,w)
@@ -60,7 +61,8 @@ Three attributes are used (south, west, radius).
\end{Verbatim}
\end{minipage}
\begin{minipage}{0.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .5
z.a = point: new (1, 1)
z.b = point: new (5, 4)
@@ -70,16 +72,16 @@ Three attributes are used (south, west, radius).
r = C.ab.radius
z.c = C.ab.opp
z.r,z.t = get_points (C.ab.ct : ortho_from (z.b))
-\end{tkzelements}
+}
-\emph{\begin{tikzpicture}
+\hfill\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPoints(a,b,c,s,w)
\tkzLabelPoints(a,b,c,s,w)
\tkzDrawCircle(a,b)
\tkzDrawSegments(a,b r,t b,c)
\tkzLabelSegment[sloped](a,b){ab = \tkzUseLua{r}}
-\end{tikzpicture}}
+\end{tikzpicture}
\end{minipage}
% subsubsection example_circle_attributes (end)
@@ -127,7 +129,7 @@ Three attributes are used (south, west, radius).
\midrule
\textbf{Miscellaneous} &&\\
\midrule
-\Imeth{circle}{power (pt)} &| r = C.OA: power (z.M)| & [\ref{par:power_v1} ; \ref{par:power_v2} ; \ref{sub:apollonius_circle_v1_with_inversion} ] \\
+\Imeth{circle}{power (pt)} &| r = C.OA: power (z.M)| & [\ref{ssub:power_v1} ; \ref{ssub:power_v2} ; \ref{sub:apollonius_circle_v1_with_inversion} ] \\
\Imeth{circle}{in\_out (pt)} & |C.OA : in_out (z.M)| & [\ref{ssub:in_out_for_circle_and_disk}] \\
\Imeth{circle}{in\_out\_disk (pt)} & |C.OA : in_out_disk (z.M)| & [\ref{ssub:in_out_for_circle_and_disk}] \\
\Imeth{circle}{draw ()} & for further use &\\
@@ -145,11 +147,12 @@ A circle is defined by its centre and a point through which it passes.
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (2,1)
C = circle: new (z.O , z.A)
-\end{tkzelements}
+}
\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawCircles(O,A)
@@ -159,11 +162,12 @@ C = circle: new (z.O , z.A)
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (2,1)
C = circle: new (z.O , z.A)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}[gridded]
\tkzGetNodes
@@ -186,12 +190,13 @@ We define a circle with its centre and radius.
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (2,1)
C = circle: radius (z.A , math.sqrt(5))
z.T = C.through
-\end{tkzelements}
+}
\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawCircles(A,T)
@@ -201,12 +206,13 @@ z.T = C.through
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (2,1)
C = circle: radius (z.A , math.sqrt(5))
z.T = C.through
- \end{tkzelements}
+ }
\begin{center}
\begin{tikzpicture}[gridded]
\tkzGetNodes
@@ -226,13 +232,14 @@ A circle is defined by two points at the ends of one of its diameters.
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.B = point: new (2,1)
C = circle: diameter (z.A , z.B)
z.O = C.center
z.T = C.through
-\end{tkzelements}
+}
\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawCircles(O,T)
@@ -242,13 +249,14 @@ z.T = C.through
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.B = point: new (2,1)
C = circle: diameter (z.A , z.B)
z.O = C.center
z.T = C.through
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}[gridded]
\tkzGetNodes
@@ -267,12 +275,13 @@ This method is used to define a point that is diametrically opposed to a point o
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.O = point: new (2,1)
C = circle: new (z.O , z.A)
z.B = C : antipode (z.A)
-\end{tkzelements}
+}
\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawCircles(O,A)
@@ -282,12 +291,13 @@ z.B = C : antipode (z.A)
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.O = point: new (2,1)
C = circle: new (z.O , z.A)
z.B = C : antipode (z.A)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}[gridded]
\tkzGetNodes
@@ -311,13 +321,14 @@ The definition I use here is more general: the defined point is simply the point
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.O = point: new (2,1)
C = circle: new (z.O , z.A)
z.B = C : point (0.25)
z.M = C : midarc (z.A,z.B)
-\end{tkzelements}
+}
\begin{tikzpicture}[gridded]
\tkzGetNodes
\tkzDrawCircles(O,A)
@@ -327,13 +338,14 @@ z.M = C : midarc (z.A,z.B)
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point: new (0,0)
z.O = point: new (2,1)
C = circle: new (z.O , z.A)
z.B = C : point (0.25)
z.M = C : midarc (z.A,z.B)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}[gridded]
\tkzGetNodes
@@ -358,14 +370,15 @@ If $r=.5$ the defined point is diametrically opposed to $A$, the angle $\widehat
\vspace{6pt}
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (1,2)
C.OA = circle: new (z.O,z.A)
z.B = C.OA: point (1/6)
z.C = C.OA: point (0.25)
z.D = C.OA: point (0.5)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle(O,A)
@@ -375,14 +388,15 @@ If $r=.5$ the defined point is diametrically opposed to $A$, the angle $\widehat
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.O = point: new (0,0)
z.A = point: new (1,2)
C.OA = circle: new (z.O,z.A)
z.B = C.OA: point (1/6)
z.C = C.OA: point (0.25)
z.D = C.OA: point (0.5)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
\tkzGetNodes
@@ -409,14 +423,15 @@ The \code{inversion} method can be used on a point, a group of points, a line or
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.o = point: new (-1,2)
z.a = point: new (2,1)
C.oa = circle: new (z.o,z.a)
z.c = point: new (3,4)
z.d = C.oa: inversion (z.c)
p = C.oa: power (z.c)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle(o,a)
@@ -429,7 +444,8 @@ The \code{inversion} method can be used on a point, a group of points, a line or
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale =.75
z.o = point: new (-1,2)
z.a = point: new (2,1)
@@ -437,7 +453,7 @@ The \code{inversion} method can be used on a point, a group of points, a line or
z.c = point: new (3,4)
z.d = C.oa: inversion (z.c)
p = C.oa: power (z.c)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -460,7 +476,8 @@ The result is either a straight line or a circle.
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.o = point: new (-1,1)
z.a = point: new (1,3)
C.oa = circle: new (z.o,z.a)
@@ -469,7 +486,7 @@ The result is either a straight line or a circle.
L.cd = line: new (z.c,z.d)
C.OH = C.oa: inversion (L.cd)
z.O,z.H = get_points(C.OH)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(o,a O,H)
@@ -480,7 +497,8 @@ The result is either a straight line or a circle.
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.o = point: new (-1,1)
z.a = point: new (1,3)
C.oa = circle: new (z.o,z.a)
@@ -489,7 +507,7 @@ The result is either a straight line or a circle.
L.cd = line: new (z.c,z.d)
C.OH = C.oa: inversion (L.cd)
z.O,z.H = get_points(C.OH)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -511,7 +529,8 @@ The result is either a straight line or a circle.
\begin{minipage}{.55\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .7
z.o,z.a = point: new (-1,3),point: new (2,3)
z.c = point: new (-2,1)
@@ -528,7 +547,7 @@ if obj.type == "line"
then z.p,z.q = get_points(obj)
else z.f,z.b = get_points(obj) end
color = "orange"
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[black](o,a)
@@ -541,7 +560,8 @@ color = "orange"
\end{Verbatim}
\end{minipage}
\begin{minipage}{.45\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
scale = .7
z.o,z.a = point: new (-1,3),point: new (2,3)
z.c = point: new (-2,1)
@@ -558,7 +578,7 @@ color = "orange"
then z.p,z.q = get_points(obj)
else z.f,z.b = get_points(obj) end
color = "orange"
- \end{tkzelements}
+ }
\begin{center}
\begin{tikzpicture}
@@ -582,8 +602,9 @@ Circles are geometrically similar to one another and mirror symmetric. Hence, a
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
- scale = 0.75
+\directlua{%
+init_elements ()
+ scale = 0.7
z.A = point : new ( 0 , 0 )
z.a = point : new ( 2 , 2 )
z.B = point : new ( 5 , 2 )
@@ -594,7 +615,7 @@ z.I = C.Aa : internal_similitude (C.Bb)
L.TA1,L.TA2 = C.Aa : tangent_from (z.I)
z.A1 = L.TA1.pb
z.A2 = L.TA2.pb
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(A,a B,b)
@@ -604,8 +625,9 @@ z.A2 = L.TA2.pb
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
- scale = .75
+\directlua{%
+init_elements ()
+ scale = .7
z.A = point : new ( 0 , 0 )
z.a = point : new ( 2 , 2 )
z.B = point : new ( 5 , 2 )
@@ -616,7 +638,7 @@ z.I = C.Aa : internal_similitude (C.Bb)
L.TA1,L.TA2 = C.Aa : tangent_from (z.I)
z.A1 = L.TA1.pb
z.A2 = L.TA2.pb
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
\tkzGetNodes
@@ -634,46 +656,48 @@ z.A2 = L.TA2.pb
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 0 , 0 )
z.a = point : new ( 2 , 2 )
z.B = point : new ( 3 , 2 )
-z.b = point : new ( 4 , 1 )
+z.b = point : new ( 3.5 , 1 )
C.Aa = circle : new (z.A,z.a)
C.Bb = circle : new (z.B,z.b)
z.I = C.Aa : external_similitude (C.Bb)
L.TA1,L.TA2 = C.Aa : tangent_from (z.I)
z.A1 = L.TA1.pb
z.A2 = L.TA2.pb
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(A,a B,b)
\tkzDrawPoints(A,a,B,b,I,A1,A2)
-\tkzDrawLines[add = .5 and .2](A1,I A2,I)
+\tkzDrawLines[add = .25 and .1](A1,I A2,I)
\end{tikzpicture}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .75
z.A = point : new ( 0 , 0 )
-z.a = point : new ( 2 , 2 )
+z.a = point : new ( 2 , 2 )
z.B = point : new ( 3 , 2 )
-z.b = point : new ( 4 , 1 )
+z.b = point : new ( 3.5, 1 )
C.Aa = circle : new (z.A,z.a)
C.Bb = circle : new (z.B,z.b)
z.I = C.Aa : external_similitude (C.Bb)
L.TA1,L.TA2 = C.Aa : tangent_from (z.I)
z.A1 = L.TA1.pb
z.A2 = L.TA2.pb
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(A,a B,b)
\tkzDrawPoints(A,a,B,b,I,A1,A2)
-\tkzDrawLines[add = .5 and .2](A1,I A2,I)
+\tkzDrawLines[add = .25 and .1](A1,I A2,I)
\end{tikzpicture}
\end{center}
\end{minipage}
@@ -691,7 +715,9 @@ Here I have also named \code{radical\_center} the point of intersection of the r
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
+ scale = .8
z.O = point : new (0,0)
z.x = point : new (1,0)
z.y = point : new (4,0)
@@ -705,12 +731,12 @@ Here I have also named \code{radical\_center} the point of intersection of the r
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)
+ % z.X = intersection (L.aap,L.bbp)
z.X = C.Ox : radical_center(C.Pz,C.Opy)
- -- L.OOp = line : new (z.O,z.Op)
- -- z.H = L.OOp : projection (z.X)
+ % L.OOp = line : new (z.O,z.Op)
+ % z.H = L.OOp : projection (z.X)
z.H = C.Ox : radical_center(C.Opy)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(O,a O',b P,z)
@@ -721,7 +747,9 @@ Here I have also named \code{radical\_center} the point of intersection of the r
\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{tkzelements}
+\directlua{%
+init_elements ()
+scale = .8
z.O = point : new (0,0)
z.x = point : new (1,0)
z.y = point : new (4,0)
@@ -738,7 +766,7 @@ 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{center}
\begin{tikzpicture}
@@ -763,7 +791,8 @@ The radical line, also called the radical axis, is the locus of points of equal
\label{par:radical_axis_v1}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .75
z.X = point : new (0,0)
z.B = point : new (2,2)
@@ -782,7 +811,7 @@ 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')
@@ -793,7 +822,8 @@ z.H = L.XY : projection (z.M)
\end{tikzpicture}
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .75
z.X = point : new (0,0)
z.B = point : new (2,2)
@@ -812,7 +842,7 @@ 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{center}
\begin{tikzpicture}
@@ -830,7 +860,8 @@ z.H = L.XY : projection (z.M)
\label{par:radical_axis_v2}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = 1.25
z.O = point : new (-1,0)
z.Op = point : new (4,-1)
@@ -847,12 +878,12 @@ _,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(E,F)
- \tkzDrawLine[add=.5 and .5](O,O')
+ \tkzDrawLine[add=.25 and .25](O,O')
\tkzDrawLines[add = 0 and .5](M,T M,T' M,K M,K')
\tkzDrawCircle(M,T)
\tkzDrawPoints(O,O',T,M,T',K,K')
@@ -860,7 +891,8 @@ _,z.Kp = get_points (L.MKp)
\end{tikzpicture}
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale =1.25
z.O = point : new (-1,0)
z.Op = point : new (4,-1)
@@ -877,14 +909,14 @@ _,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{center}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(O,B O',D)
\tkzDrawLine(E,F)
- \tkzDrawLine[add=.5 and .5](O,O')
+ \tkzDrawLine[add=.25 and .25](O,O')
\tkzDrawLines[add = 0 and .5](M,T M,T' M,K M,K')
\tkzDrawCircle(M,T)
\tkzDrawPoints(O,O',T,M,T',K,K')
@@ -897,7 +929,8 @@ _,z.Kp = get_points (L.MKp)
\label{par:radical_axis_v3}
\begin{Verbatim}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.O = point : new (0,0)
z.B = point : new (4,0)
z.Op = point : new (6,0)
@@ -910,7 +943,7 @@ _,z.Kp = get_points (L.MKp)
_,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)
@@ -923,7 +956,8 @@ _,z.Kp = get_points (L.MKp)
\end{tikzpicture}
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.B = point : new (4,0)
z.Op = point : new (6,0)
@@ -936,7 +970,7 @@ 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{center}
\begin{tikzpicture}
@@ -956,7 +990,8 @@ _,z.Tp = get_points (L)
\label{par:radical_axis_v4}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.B = point : new (5,0)
z.Op = point : new (3,0)
@@ -970,7 +1005,7 @@ _,z.Tp = get_points (L)
_,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)
@@ -983,7 +1018,8 @@ _,z.Tp = get_points (L)
\end{tikzpicture}
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.B = point : new (5,0)
z.Op = point : new (3,0)
@@ -997,7 +1033,7 @@ _,z.Tp = get_points (L)
_,z.T = get_points (L)
_,L = C.OpB : tangent_from (z.M)
_,z.Tp = get_points (L)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -1021,7 +1057,8 @@ _,z.Tp = get_points (L)
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.A = point: new (0,0)
z.B = point: new (1,2)
C.AB = circle: new (z.A,z.B)
@@ -1031,7 +1068,7 @@ _,z.Tp = get_points (L)
L.T1,L.T2 = C.AB : tangent_from (z.C)
z.T1 = L.T1.pb
z.T2 = L.T2.pb
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle(A,B)
@@ -1045,7 +1082,8 @@ _,z.Tp = get_points (L)
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.A = point: new (0,0)
z.B = point: new (1,2)
C.AB = circle: new (z.A,z.B)
@@ -1055,7 +1093,7 @@ _,z.Tp = get_points (L)
L.T1,L.T2 = C.AB : tangent_from (z.C)
z.T1 = L.T1.pb
z.T2 = L.T2.pb
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
\tkzGetNodes
@@ -1078,7 +1116,8 @@ _,z.Tp = get_points (L)
Let be a tangent common to both circles at $T$ and $T'$ (closest to $C$). Let a secant parallel to this tangent pass through $C$. Then the segment $[TT']$ is seen from the other common point $D$ at an angle equal to half the angle of the two circles.
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 0 , 0 )
z.B = point : new ( 5 , 2 )
L.AB = line : new ( z.A , z.B )
@@ -1094,7 +1133,7 @@ Let be a tangent common to both circles at $T$ and $T'$ (closest to $C$). Let a
_,z.M = intersection (L.mm, C.AC)
z.Mp = intersection (L.mm, C.BC)
_,z.D = intersection (C.AC,C.BC)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles(A,C B,C)
@@ -1109,7 +1148,8 @@ Let be a tangent common to both circles at $T$ and $T'$ (closest to $C$). Let a
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 0 , 0 )
z.B = point : new ( 5 , 2 )
L.AB = line : new ( z.A , z.B )
@@ -1125,7 +1165,7 @@ L.mm = L.TTp : ll_from (z.C)
_,z.M = intersection (L.mm, C.AC)
z.Mp = intersection (L.mm, C.BC)
_,z.D = intersection (C.AC,C.BC)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -1150,14 +1190,15 @@ In geometry, two circles are said to be orthogonal if their respective tangent l
This method determines a circle with a given centre, orthogonal to a circle that is also given.
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
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)
@@ -1176,14 +1217,15 @@ This method determines a circle with a given centre, orthogonal to a circle that
\end{tikzpicture}
\end{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
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{center}
\begin{tikzpicture}
@@ -1210,7 +1252,8 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point: new (0,1)
z.A = point: new (1,0)
z.z1 = point: new (-1.5,-1.5)
@@ -1218,7 +1261,7 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
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)
@@ -1228,7 +1271,8 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\end{tikzpicture}
\end{Verbatim}
\end{minipage}
-\begin{minipage}{.5\textwidth}\begin{tkzelements}
+\begin{minipage}{.5\textwidth}\directlua{%
+init_elements ()
z.O = point: new (0,1)
z.A = point: new (1,0)
z.z1 = point: new (-1.5,-1.5)
@@ -1236,7 +1280,7 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
C.OA = circle: new (z.O,z.A)
C = C.OA: orthogonal_through (z.z1,z.z2)
z.c = C.center
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -1274,7 +1318,8 @@ We can obtain the centers of similarity of these two circles by constructing $EH
\begin{minipage}{.4\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .8
z.A = point : new ( 1 , 0 )
z.B = point : new ( 3 , 0 )
@@ -1290,11 +1335,12 @@ C.IT,C.JV = C.AO : midcircle (C.BP)
z.I,z.T = get_points (C.IT)
z.J,z.V = get_points (C.JV)
z.X,z.Y = intersection (C.AO,C.BP)
-\end{tkzelements}
+}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
scale = .8
z.A = point : new ( 1 , 0 )
z.B = point : new ( 3 , 0 )
@@ -1310,7 +1356,7 @@ z.X,z.Y = intersection (C.AO,C.BP)
z.I,z.T = get_points (C.IT)
z.J,z.V = get_points (C.JV)
z.X,z.Y = intersection (C.AO,C.BP)
- \end{tkzelements}
+ }
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[teal,thick](A,O B,P)
@@ -1337,7 +1383,8 @@ z.X,z.Y = intersection (C.AO,C.BP)
\label{midcircle_diameter}
\begin{minipage}{.6\textwidth}
\begin{Verbatim}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
scale =.75
z.A = point : new ( 3 , 0 )
z.B = point : new ( 5 , 0 )
@@ -1354,11 +1401,12 @@ z.X,z.Y = intersection (C.AO,C.BP)
z.y = C.UR.center
C.IT = C.AO : midcircle (C.BP)
z.I,z.T = get_points (C.IT)
-\end{tkzelements}
+}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
scale =.75
z.A = point : new ( 3 , 0 )
z.B = point : new ( 5 , 0 )
@@ -1375,7 +1423,7 @@ z.X,z.Y = intersection (C.AO,C.BP)
z.y = C.UR.center
C.IT = C.AO : midcircle (C.BP)
z.I,z.T = get_points (C.IT)
- \end{tkzelements}
+ }
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[teal,thick](A,O B,P)
@@ -1397,7 +1445,8 @@ $I$ is the center of external similarity of the two given circles. To obtain the
\begin{minipage}{.4\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale=.75
local a,b,c,d
z.A = point : new ( 0 , 0 )
@@ -1416,11 +1465,12 @@ L.TF = C.Bb : tangent_from (z.I)
z.H = intersection (L.TF,C.IT)
z.E = intersection (L.TF,C.Aa)
z.F=L.TF.pb
-\end{tkzelements}
+}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale=.75
local a,b,c,d
z.A = point : new ( 0 , 0 )
@@ -1439,7 +1489,7 @@ L.TF = C.Bb : tangent_from (z.I)
z.H = intersection (L.TF,C.IT)
z.E = intersection (L.TF,C.Aa)
z.F=L.TF.pb
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[teal,thick](A,a B,b)
@@ -1462,7 +1512,8 @@ z.F=L.TF.pb
\begin{minipage}{.4\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale=.75
local a,b,c,d
z.A = point : new ( 0 , 0 )
@@ -1481,11 +1532,12 @@ L.TF = C.Bb : tangent_from (z.I)
z.H = intersection (L.TF,C.IT)
z.E = intersection (L.TF,C.Aa)
z.F=L.TF.pb
-\end{tkzelements}
+}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale=.75
local a,b,c,d
z.A = point : new ( 0 , 0 )
@@ -1504,7 +1556,7 @@ L.TF = C.Bb : tangent_from (z.I)
z.H = intersection (L.TF,C.IT)
z.E = intersection (L.TF,C.Aa)
z.F=L.TF.pb
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[teal,thick](A,a B,b)
@@ -1524,7 +1576,8 @@ z.F=L.TF.pb
\begin{minipage}{.4\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 2 , 0 )
z.B = point : new ( 4 , 0 )
z.a = point : new ( 1 , 0)
@@ -1533,11 +1586,12 @@ C.Aa = circle : new (z.A,z.a)
C.Bb = circle : new (z.B,z.b)
C.IT = C.Aa : midcircle (C.Bb)
z.I,z.T = get_points(C.IT)
-\end{tkzelements}
+}
\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 2 , 0 )
z.B = point : new ( 4 , 0 )
z.a = point : new ( 1 , 0)
@@ -1546,7 +1600,7 @@ C.Aa = circle : new (z.A,z.a)
C.Bb = circle : new (z.B,z.b)
C.IT = C.Aa : midcircle (C.Bb)
z.I,z.T = get_points (C.IT)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
@@ -1569,7 +1623,8 @@ z.I,z.T = get_points (C.IT)
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .5
z.A = point: new (0,0)
z.B = point: new (6,0)
@@ -1583,7 +1638,7 @@ z.I,z.T = get_points (C.IT)
z.I_c,z.Xc = get_points (C.exc)
C.ortho = C.exa : radical_circle (C.exb,C.exc)
z.w,z.a = get_points (C.ortho)
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPolygon(A,B,C)
@@ -1595,7 +1650,8 @@ z.I,z.T = get_points (C.IT)
\end{Verbatim}
\end{minipage}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
scale = .5
z.A = point: new (0,0)
z.B = point: new (6,0)
@@ -1609,7 +1665,7 @@ z.I,z.T = get_points (C.IT)
z.I_c,z.Xc = get_points (C.exc)
C.ortho = C.exa : radical_circle (C.exb,C.exc)
z.w,z.a = get_points (C.ortho)
-\end{tkzelements}
+}
\begin{center}
\begin{tikzpicture}
@@ -1623,14 +1679,14 @@ z.I,z.T = get_points (C.IT)
\end{center}
% subsubsection radical_circle (end)
-\subsubsection{Method \Imeth{circle}{power(C)}} % (fold)
-\label{ssub:method_imeth_circle_power_c}
+\subsubsection{Method \Imeth{circle}{power(C)} Power v1} % (fold)
+\label{ssub:power_v1}
-\paragraph{Power v1} % (fold)
-\label{par:power_v1}
-\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
+
+\begin{minipage}[t]{.45\textwidth}\vspace{0pt}%
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.A = point : new (2,-2)
z.M = point : new (-6,0)
@@ -1638,7 +1694,7 @@ z.I,z.T = get_points (C.IT)
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)
@@ -1650,9 +1706,10 @@ z.I,z.T = get_points (C.IT)
\end{tikzpicture}
\end{Verbatim}
\end{minipage}
-\begin{minipage}[t]{.5\textwidth}
-\begin{tkzelements}
-scale = 1
+\begin{minipage}[t]{.55\textwidth}\vspace{0pt}%
+\directlua{%
+init_elements ()
+scale = .75
z.O = point : new (0,0)
z.A = point : new (2,-2)
z.M = point : new (-6,0)
@@ -1660,11 +1717,8 @@ 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{center}
- \begin{tikzpicture}
+}
+\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle(O,A)
\tkzMarkRightAngle[fill=gray!10](A',B,M)
@@ -1673,16 +1727,18 @@ z.B = intersection (L.AM, C.OA)
\tkzLabelPoints(O,A,A',M,B)
\tkzDrawSegments[-Triangle](M,A M,A')
\end{tikzpicture}
-\end{center}
-
\end{minipage}
-% paragraph power_v1 (end)
+% subsubsection power_v1 (end)
+
+\subsubsection{Method \Imeth{circle}{power(C)} Power v2} % (fold)
+\label{ssub:power_v2}
+\vspace{6pt}
+
-\paragraph{Power v2} % (fold)
-\label{par:power_v2}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.A = point : new (2,2)
z.M = point : new (-1.5,0)
@@ -1693,7 +1749,7 @@ 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)
@@ -1707,8 +1763,9 @@ z.B = intersection (L.AM, C.OA)
\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{tkzelements}
-scale = 1
+\directlua{%
+init_elements ()
+scale = .8
z.O = point : new (0,0)
z.A = point : new (2,2)
z.M = point : new (-1.5,0)
@@ -1719,7 +1776,7 @@ _,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{center}
\begin{tikzpicture}
@@ -1735,7 +1792,7 @@ z.U,z.V = intersection (L.mM,C.OA)
\end{center}
\end{minipage}
-% paragraph power_v2 (end)
+% subsubsection power_v2 (end)
% subsubsection method_imeth_circle_power_c (end)
@@ -1744,7 +1801,8 @@ z.U,z.V = intersection (L.mM,C.OA)
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
- \begin{tkzelements}
+ \directlua{%
+init_elements ()
z.O = point : new (0,0)
z.A = point : new (1,2)
C.OA = circle : new (z.O,z.A)
@@ -1757,10 +1815,11 @@ z.U,z.V = intersection (L.mM,C.OA)
BDn = C.OA : in_out_disk (z.N)
BCp = C.OA : in_out (z.P)
BDp = C.OA : in_out_disk (z.P)
- \end{tkzelements}
+ }
\end{Verbatim}
\end{minipage}
-\begin{minipage}{.5\textwidth}\begin{tkzelements}
+\begin{minipage}{.5\textwidth}\directlua{%
+init_elements ()
z.O = point : new (0,0)
z.A = point : new (1,2)
C.OA = circle : new (z.O,z.A)
@@ -1773,7 +1832,7 @@ BCn = C.OA : in_out (z.N)
BDn = C.OA : in_out_disk (z.N)
BCp = C.OA : in_out (z.P)
BDp = C.OA : in_out_disk (z.P)
-\end{tkzelements}
+}
\def\tkzPosPoint#1#2#3#4{%
\tkzLabelPoints(O,M,N,P)
\ifthenelse{\equal{\tkzUseLua{#1}}{true}}{
@@ -1835,7 +1894,8 @@ This function returns a string indicating the position of the circle in relation
\begin{minipage}{.5\textwidth}
\begin{Verbatim}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 0 , 0 )
z.a = point : new ( 3 , 0 )
z.B = point : new ( 2 , 0 )
@@ -1846,7 +1906,7 @@ This function returns a string indicating the position of the circle in relation
if position == "inside tangent"
then color = "orange"
else color = "blue" end
-\end{tkzelements}
+}
\begin{tikzpicture}
\tkzGetNodes
@@ -1856,7 +1916,8 @@ This function returns a string indicating the position of the circle in relation
\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
-\begin{tkzelements}
+\directlua{%
+init_elements ()
z.A = point : new ( 1 , 0 )
z.a = point : new ( 3 , 0 )
z.B = point : new ( 2 , 0 )
@@ -1865,7 +1926,7 @@ C.Aa = circle: new (z.A,z.a)
C.Bb = circle: new (z.B,z.b)
position = C.Aa : circles_position (C.Bb)
if position == "inside tangent" then color = "orange" else color = "blue" end
-\end{tkzelements}
+}
\hspace{\fill}
\begin{tikzpicture}
\tkzGetNodes