summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
diff options
context:
space:
mode:
Diffstat (limited to 'macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex')
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex225
1 files changed, 222 insertions, 3 deletions
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
index f54a53f39e..80b711e46f 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
@@ -202,7 +202,9 @@ Through the Lemoine point draw lines parallel to the triangle's sides. The point
then lie on a circle known as the first Lemoine circle. } \\
\Imeth{triangle}{second\_lemoine\_circle ()} & Refer to example \ref{sub:antiparallel_through_lemoine_point}\\
\Imeth{triangle}{spieker\_circle ()} & The incircle of the medial triangle\\
-
+\Imeth{triangle}{cevian\_circle ()} & Circumscribed circle of a Cevian triangle Refer to (\ref{ssub:method_imeth_triangle_cevian})\\
+\Imeth{triangle}{pedal\_circle ()} & Circumscribed circle of the podar triangle Refer to (\ref{ssub:method_imeth_triangle_pedal})\\
+\Imeth{triangle}{conway\_circle ()} & Circumscribed circle of Conway points Refer to (\ref{ssub:method_imeth_triangle_conway})\\
\bottomrule
\end{tabular}
\end{minipage}
@@ -234,7 +236,8 @@ Remark: If you don't need to use the triangle object several times, you can obta
\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}{cevian (pt)} & Triangle formed with the endpoints of the three cevians with respect to |pt|. refer to (\ref{ssub:method_imeth_triangle_cevian})\\
+\Imeth{triangle}{pedal (pt)} & Triangle formed by projections onto the sides of |pt| Refer to \ref{ssub:method_imeth_triangle_pedal}\\
\Imeth{triangle}{symmedian ()} & Triangle formed with the intersection points of the symmedians. \\
\Imeth{triangle}{euler ()} & Triangle formed with the euler points \\
\midrule
@@ -256,6 +259,171 @@ Remark: If you don't need to use the triangle object several times, you can obta
\egroup
% subsubsection methods_of_the_class_triangle (end)
+
+\subsubsection{Méthodes \Imeth{triangle}{cevian} et \Imeth{triangle}{cevian\_circle}} % (fold)
+\label{ssub:method_imeth_triangle_cevian}
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+ scale = 2
+ z.a = point: new (1,2)
+ z.b = point: new (5,1)
+ z.c = point: new (3,5)
+ T = triangle: new (z.a,z.b,z.c)
+ z.i = T.orthocenter
+ T.cevian = T : cevian (z.i)
+ z.ta,z.tb,z.tc = get_points (T.cevian)
+ C.cev = T : cevian_circle (z.i)
+ z.w = C.cev.center
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(a,b,c ta,tb,tc)
+\tkzDrawSegments(a,ta b,tb c,tc)
+\tkzDrawPoints(a,b,c,i,ta,tb,tc)
+\tkzLabelPoints(a,b,c,i)
+\tkzDrawCircles(w,ta)
+\end{tikzpicture}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+\begin{tkzelements}
+scale = 2
+z.a = point: new (1,2)
+z.b = point: new (5,1)
+z.c = point: new (3,5)
+T = triangle: new (z.a,z.b,z.c)
+z.i = T.orthocenter
+T.cevian = T : cevian (z.i)
+z.ta,z.tb,z.tc = get_points (T.cevian)
+C.cev = T : cevian_circle (z.i)
+z.w = C.cev.center
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygons(a,b,c ta,tb,tc)
+\tkzDrawSegments(a,ta b,tb c,tc)
+\tkzDrawPoints(a,b,c,i,ta,tb,tc)
+\tkzLabelPoints(a,b,c,i)
+\tkzDrawCircles(w,ta)
+\end{tikzpicture}
+\end{minipage}
+% subsubsection method_imeth_triangle_cevian (end)
+
+
+\subsubsection{Méthodes \Imeth{triangle}{pedal} et \Imeth{triangle}{pedal\_circle}} % (fold)
+\label{ssub:method_imeth_triangle_pedal}
+
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+ \begin{tkzelements}
+ z.A = point: new(0,0)
+ z.B = point: new(5,0)
+ z.C = point: new(1.5,3)
+ z.O = point: new (2,1)
+ T.ABC = triangle: new (z.A,z.B,z.C)
+ T.pedal = T.ABC : pedal (z.O)
+ z.E,z.F,z.G = get_points(T.pedal)
+ C.pedal = T.ABC : pedal_circle (z.O)
+ z.w = C.pedal.center
+ z.T = C.pedal.through
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawPolygon[red](E,F,G)
+ \tkzDrawCircle(w,T)
+ \tkzDrawPoints(A,B,C,E,F,G,O)
+ \tkzLabelPoints(A,B,C,E,F,G)
+ \tkzDrawSegments(O,E O,F O,G)
+ \end{tikzpicture}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \begin{tkzelements}
+ z.A = point: new(0,0)
+ z.B = point: new(5,0)
+ z.C = point: new(1.5,3)
+ z.O = point: new (2,1)
+ T.ABC = triangle: new (z.A,z.B,z.C)
+ T.pedal = T.ABC : pedal (z.O)
+ z.E,z.F,z.G = get_points(T.pedal)
+ C.pedal = T.ABC : pedal_circle (z.O)
+ z.w = C.pedal.center
+ z.T = C.pedal.through
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawPolygon[red](E,F,G)
+ \tkzDrawCircle(w,T)
+ \tkzDrawPoints(A,B,C,E,F,G,O)
+ \tkzLabelPoints(A,B,C,E,F,G)
+ \tkzDrawSegments(O,E O,F O,G)
+ \end{tikzpicture}
+\end{minipage}
+% subsubsection method_imeth_triangle_pedal (end)
+
+\subsubsection{Méthodes \Imeth{triangle}{conway\_points} et \Imeth{triangle}{conway\_circle}} % (fold)
+\label{ssub:method_imeth_triangle_conway}
+
+En géométrie plane, le théorème du cercle de Conway stipule que lorsque les côtés se rencontrant à chaque sommet d'un triangle sont prolongés par la longueur du côté opposé, les six points d'extrémité des trois segments de droite résultants se trouvent sur un cercle dont le centre est le centre d'incidence du triangle.
+
+\begin{minipage}{.5\textwidth}
+ \begin{Verbatim}
+ \begin{tkzelements}
+ z.A = point:new (0,0)
+ z.C = point:new (5,0)
+ z.B = point:new (1,3)
+ T.ABC = triangle : new (z.A,z.B,z.C)
+ C.conway = T.ABC : conway_circle ()
+ z.w,z.t = get_points(C.conway)
+ z.t1,z.t2,z.t3,z.t4,
+ z.t5,z.t6= T.ABC : conway_points ()
+ \end{tkzelements}
+ \hspace*{5cm}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawCircles(w,t)
+ \tkzDrawPoints(t1,t2,t3,t4,t5,t6)
+ \tkzLabelPoints(t1,t2,t3,t4,t5,t6)
+ \tkzDrawSegments[dashed](t1,A t2,A t3,B)
+ \tkzDrawSegments[dashed](t4,B t5,C t6,C)
+ \tkzMarkSegments(B,C t1,A t2,A)
+ \tkzMarkSegments[mark=||](A,C t3,B t4,B)
+ \tkzMarkSegments[mark=|||](A,B t5,C t6,C)
+ \end{tikzpicture}
+ \end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \begin{tkzelements}
+ scale = .5
+ z.A = point:new (0,0)
+ z.C = point:new (5,0)
+ z.B = point:new (1,3)
+ T.ABC = triangle : new (z.A,z.B,z.C)
+ C.conway = T.ABC : conway_circle ()
+ z.w,z.t = get_points(C.conway)
+ z.t1,z.t2,z.t3,
+ z.t4,z.t5,z.t6= T.ABC : conway_points ()
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawCircles(w,t)
+ \tkzDrawPoints(t1,t2,t3,t4,t5,t6)
+ \tkzLabelPoints(t1,t2,t3,t4,t5,t6)
+ \tkzDrawSegments[dashed](t1,A t2,A t3,B t4,B t5,C t6,C)
+ \tkzMarkSegments(B,C t1,A t2,A)
+ \tkzMarkSegments[mark=||](A,C t3,B t4,B)
+ \tkzMarkSegments[mark=|||](A,B t5,C t6,C)
+ \end{tikzpicture}
+\end{minipage}
+
+% subsubsection methode_imeth_triangle_conway (end)
+
+
\subsubsection{Euler line} % (fold)
\label{ssub:euler_line}
@@ -549,10 +717,61 @@ z.T2 = L.T2.pb
\tkzMarkSegments(B,E B,M B,F)
\end{tikzpicture}
\end{Verbatim}
+% subsection harmonic_division_and_bisector (end)
+
+\subsubsection{Method \Imeth{triangle}{cevan}} % (fold)
+\label{ssub:method_imeth_triangle_cevan}
+
+\begin{minipage}{.5\textwidth}
+ \begin{Verbatim}
+ \begin{tkzelements}
+ scale = 2
+ z.a = point: new (1,2)
+ z.b = point: new (5,1)
+ z.c = point: new (3,5)
+ T = triangle: new (z.a,z.b,z.c)
+ z.i = T.orthocenter
+ T.cevian = T : cevian (z.i)
+ z.ta,z.tb,z.tc = get_points (T.cevian)
+ C.cev = T : cevian_circle (z.i)
+ z.w = C.cev.center
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygons(a,b,c ta,tb,tc)
+ \tkzDrawSegments(a,ta b,tb c,tc)
+ \tkzDrawPoints(a,b,c,i,ta,tb,tc)
+ \tkzLabelPoints(a,b,c,i)
+ \tkzDrawCircles(w,ta)
+ \end{tikzpicture}
+ \end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \begin{tkzelements}
+ scale = 2
+ z.a = point: new (1,2)
+ z.b = point: new (5,1)
+ z.c = point: new (3,5)
+ T = triangle: new (z.a,z.b,z.c)
+ z.i = T.orthocenter
+ T.cevian = T : cevian (z.i)
+ z.ta,z.tb,z.tc = get_points (T.cevian)
+ C.cev = T : cevian_circle (z.i)
+ z.w = C.cev.center
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygons(a,b,c ta,tb,tc)
+ \tkzDrawSegments(a,ta b,tb c,tc)
+ \tkzDrawPoints(a,b,c,i,ta,tb,tc)
+ \tkzLabelPoints(a,b,c,i)
+ \tkzDrawCircles(w,ta)
+ \end{tikzpicture}
+\end{minipage}
+% subsubsection method_imeth_triangle_cevan (end)
-% subsection harmonic_division_and_bisector (end)
% subsection methods_of_the_class_triangle (end)
% section class_triangle (end)
\endinput