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+% tkz-obj-eu-triangles.tex
+% Copyright 2019 by Alain Matthes
+% This file may be distributed and/or modified
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+\def\fileversion{3.01c}
+\def\filedate{2020/01/23}
+\typeout{2020/01/23 3.01c tkz-obj-eu-triangles.tex}
+\makeatletter
+%<--------------------------------------------------------------------------–>
+% Triangle Equilateral
+%<--------------------------------------------------------------------------–>
+\def\tkzDefEquilateral(#1,#2){
+\begingroup
+\tkzDefMidPoint(#1,#2)
+ \tkzURotateAngle(#1,60)(#2)
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+
+\def\tkzDrawEquilateral{\pgfutil@ifnextchar[{\tkz@Equilateral}{%
+ \tkz@Equilateral[]}}
+
+\def\tkz@Equilateral[#1](#2,#3){%
+\begingroup
+ \tkzURotateAngle(#2,60)(#3)
+ \tkzDrawPolygon[#1](#2,#3,tkzPointResult)
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+% Triangle OneTwo
+%<--------------------------------------------------------------------------–>
+\def\tkzPhi{1.618034}
+\def\tkzInvPhi{0.618034}
+\def\tkzSqrtPhi{1.27202}
+
+\def\tkzDefTwoOne(#1,#2){
+\begingroup
+ \tkzVecKOrth[-.5](#2,#1)
+ \endgroup
+}
+\def\tkzDefPythagore(#1,#2){
+\begingroup
+ \tkzVecKOrth[-0.75](#2,#1)
+\endgroup
+}
+\def\tkzDefSchoolTriangle(#1,#2){
+\begingroup
+ \tkzVecKOrth[-1](#2,#1)
+ \pgfnodealias{tkz@a}{tkzPointResult}
+ \tkzURotateAngle(#1,30)(#2)
+ \tkzInterLL(#1,tkzPointResult)(#2,tkz@a)
+\endgroup
+}
+\def\tkzDefGoldTriangle(#1,#2){
+\begingroup
+ \tkzURotateAngle(#1,36)(#2)
+\endgroup
+}
+\def\tkzDefEuclideTriangle(#1,#2){
+\begingroup
+ \tkzURotateAngle(#1,72)(#2)
+ \tkzUHomo(#1,\tkzPhi)(tkzPointResult)
+\endgroup
+}
+\def\tkzDefGoldenTriangle(#1,#2){
+\begingroup
+ \tkzVecKOrth[-\tkzInvPhi](#2,#1)
+\endgroup
+}
+\def\tkzDefCheopsTriangle(#1,#2){
+\begingroup
+\tkzDefMidPoint(#1,#2)
+ \tkzVecKOrth[-\tkzSqrtPhi](tkzPointResult,#1)
+\endgroup
+}
+\def\tkzDefTwoAnglesTriangle(#1,#2){
+\begingroup
+ \tkzURotateAngle(#1,\tkz@alpha)(#2)
+ \pgfnodealias{tkz@pta}{tkzPointResult}
+ \tkzURotateAngle(#2,-\tkz@beta)(#1)
+ \pgfnodealias{tkz@ptb}{tkzPointResult}
+ \tkzInterLL(#1,tkz@pta)(#2,tkz@ptb)
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+% Triangles
+%<--------------------------------------------------------------------------–>
+
+\def\tkz@numtr{0}
+\pgfkeys{%
+ /deftriangle/.cd,
+ equilateral/.code = \def\tkz@numtr{0},
+ half/.code = \def\tkz@numtr{1},
+ pythagore/.code = \def\tkz@numtr{2},
+ school/.code = \def\tkz@numtr{3},
+ golden/.code = \def\tkz@numtr{4},
+ sublime/.code = \def\tkz@numtr{4},
+ euclide/.code = \def\tkz@numtr{5},
+ gold/.code = \def\tkz@numtr{6},
+ cheops/.code = \def\tkz@numtr{7},
+ two angles/.code args = {#1 and #2} { \def\tkz@numtr{8}%
+ \def\tkz@alpha{#1}%
+ \def\tkz@beta{#2}}
+}
+
+\def\tkzDefTriangle{\pgfutil@ifnextchar[{\tkz@DefTriangle}{\tkz@DefTriangle[]}}
+\def\tkz@DefTriangle[#1](#2,#3){%
+\begingroup
+\pgfkeys{/deftriangle/.cd,equilateral}
+\pgfqkeys{/deftriangle}{#1}
+\ifcase\tkz@numtr%
+ \tkzDefEquilateral(#2,#3)
+ \or% 1
+ \tkzDefTwoOne(#2,#3)
+ \or% 2
+ \tkzDefPythagore(#2,#3)
+ \or% 3
+ \tkzDefSchoolTriangle(#2,#3)
+ \or% 4
+ \tkzDefGoldenTriangle(#2,#3)
+ \or% 5
+ \tkzDefEuclideTriangle(#2,#3)
+ \or% 6
+ \tkzDefGoldTriangle(#2,#3)
+ \or% 7
+ \tkzDefCheopsTriangle(#2,#3)
+ \or% 8
+ \tkzDefTwoAnglesTriangle(#2,#3) \fi
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+% Draw Triangles
+%<--------------------------------------------------------------------------–>
+
+\def\tkz@numdtr{0}
+\pgfkeys{/drawtriangle/.cd,
+ equilateral/.code = {\def\tkz@numdtr{0}},
+ half/.code = {\def\tkz@numdtr{1}},
+ pythagore/.code = {\def\tkz@numdtr{2}},
+ school/.code = {\def\tkz@numdtr{3}},
+ golden/.code = {\def\tkz@numdtr{4}},
+ sublime/.code = {\def\tkz@numdtr{4}},
+ euclide/.code = {\def\tkz@numdtr{5}},
+ gold/.code = {\def\tkz@numdtr{6}},
+ cheops/.code = {\def\tkz@numdtr{7}},
+ two angles/.code args = {#1 and #2}{\def\tkz@numdtr{8}%
+ \def\tkz@alpha{#1}%
+ \def\tkz@beta{#2}},
+ equilateral,
+ /drawtriangle/.search also={/tikz}
+}
+
+\def\tkzDrawTriangle{\pgfutil@ifnextchar[{\tkz@DrawTriangle}{%
+ \tkz@DrawTriangle[]}}
+\def\tkz@DrawTriangle[#1](#2,#3){%
+\begingroup
+\pgfkeys{/drawtriangle/.cd,equilateral}
+\pgfqkeys{/drawtriangle}{#1}
+\ifcase\tkz@numdtr%
+ \tkzDefEquilateral(#2,#3)
+\or% 1
+ \tkzDefTwoOne(#2,#3)
+\or% 2
+ \tkzDefPythagore(#2,#3)
+\or% 3
+ \tkzDefSchoolTriangle(#2,#3)
+\or% 4
+ \tkzDefGoldenTriangle(#2,#3)
+\or% 5
+ \tkzDefEuclideTriangle(#2,#3)
+\or% 6
+ \tkzDefGoldTriangle(#2,#3)
+\or% 7
+ \tkzDefCheopsTriangle(#2,#3)
+\or% 8
+ \tkzDefTwoAnglesTriangle(#2,#3)
+\fi
+ \draw[/drawtriangle/.cd,line style,#1] (#2)--(#3)--(tkzPointResult)--cycle;
+\endgroup
+}
+
+%<--------------------------------------------------------------------------–>
+% les triangles sspécifiques
+%<--------------------------------------------------------------------------–>
+
+%<--------------------------------------------------------------------------–
+\def\tkz@numtspc{0}
+\pgfkeys{/tkzDefSpcTriangle/.cd,
+ in/.code = \def\tkz@numtspc{0},
+ incentral/.code = \def\tkz@numtspc{0},
+ ex/.code = \def\tkz@numtspc{1},
+ excentral/.code = \def\tkz@numtspc{1},
+ extouch/.code = \def\tkz@numtspc{2},
+ intouch/.code = \def\tkz@numtspc{3},
+ contact/.code = \def\tkz@numtspc{3},
+ centroid/.code = \def\tkz@numtspc{4},
+ medial/.code = \def\tkz@numtspc{4},
+ orthic/.code = \def\tkz@numtspc{5},
+ ortho/.code = \def\tkz@numtspc{5},
+ feuerbach/.code = \def\tkz@numtspc{6},
+ euler/.code = \def\tkz@numtspc{7},
+ tangential/.code = \def\tkz@numtspc{8},
+ symmedian/.code = \def\tkz@numtspc{9},
+ name/.store in = \tkz@pttr@name,
+ name = {},
+ centroid,
+ }
+\def\tkzDefSpcTriangle{\pgfutil@ifnextchar[{\tkz@DefSpcTriangle}{%
+ \tkz@DefSpcTriangle[]}}
+\def\tkz@DefSpcTriangle[#1](#2)#3{%
+\begingroup
+\pgfqkeys{/tkzDefSpcTriangle}{#1}
+\ifcase\tkz@numtspc%
+ \tkzDefIncentralTriangle(#2){#3}
+ \or% 1
+ \tkzDefExcentralTriangle(#2){#3}
+ \or% 2
+ \tkzDefExtouchTriangle(#2){#3}
+ \or% 3
+ \tkzDefIntouchTriangle(#2){#3}
+ \or% 4
+ \tkzDefCentroidTriangle(#2){#3}
+ \or% 5
+ \tkzDefOrthicTriangle(#2){#3}
+ \or% 6
+ \tkzDefFeuerbachTriangle(#2){#3}
+ \or% 7
+ \tkzDefEulerTriangle(#2){#3}
+ \or% 8
+ \tkzDefTangentialTriangle(#2){#3}
+ \or% 8
+ \tkzDefSymmedianTriangle(#2){#3}
+ \fi
+\endgroup
+}
+
+
+\pgfkeys{/setuppttr/.is family}
+\def\SetUpPTTR#1{\pgfqkeys{/setuppttr}{#1}}
+\pgfkeys{/setuppttr/.cd,
+ name/.store in = \tkz@pttr@name,
+ name = {}
+}
+\def\tkz@recuplast(#1,#2){\def\tkz@last{#1}}
+\def\tkz@stop{\tkz@stop}
+%<--------------------------------------------------------------------------–
+% InCentral
+%<--------------------------------------------------------------------------–
+% The Incentral triangle is the triangle whose vertices are determined by
+% theintersections of the reference triangle’s angle bisectors with the
+% respective opposite sides.
+%<--------------------------------------------------------------------------–>
+\def\@DefIncentralTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \tkzDefBisectorLine(#2,#1,\tkz@last)
+ \tkzInterLL(#2,\tkz@last)(#1,tkzPointResult)
+ \pgfnodealias{#4}{tkzPointResult}
+ \ifx\tkz@tmp\tkz@stop\else\@DefIncentralTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+}
+
+
+\def\tkzDefIncentralTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefIncentralTriangle}{%
+ \tkz@DefIncentralTriangle[]}}
+
+\def\tkz@DefIncentralTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \pgfinterruptboundingbox
+ \@DefIncentralTriangle(#2,#2)(#3,\tkz@stop)
+ \endpgfinterruptboundingbox
+\endgroup
+}
+\let\tkzIncentralTriangle\tkzInExcentralTriangle
+%<--------------------------------------------------------------------------–
+% ExCentral
+%<--------------------------------------------------------------------------–
+
+%<--------------------------------------------------------------------------–>
+\def\@DefExcentralTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \tkzDefExCircle(#2,#1,\tkz@last)
+ \pgfnodealias{#4}{tkzPointResult}
+ \ifx\tkz@tmp\tkz@stop\else\@DefExcentralTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+}
+
+\def\tkzDefExcentralTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefExcentralTriangle}{%
+ \tkz@DefExcentralTriangle[]}}
+
+\def\tkz@DefExcentralTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \@DefExcentralTriangle(#2,#2)(#3,\tkz@stop)
+\endgroup
+}
+\let\tkzExcentralTriangle\tkzDefExcentralTriangle
+%<--------------------------------------------------------------------------–>
+% Intouch Triangle
+% The contact triangle of a triangle ABC, also called the intouch triangle, is the triangle formed by the points of tangency of the incircle of ABC with ABC.
+%<--------------------------------------------------------------------------–>
+\def\@DefIntouchTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \tkzUProjection(#2,\tkz@last)(tkz@pt)
+ \pgfnodealias{#4}{tkzPointResult}
+ \ifx\tkz@tmp\tkz@stop\else\@DefIntouchTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+}
+
+\def\tkzDefIntouchTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefIntouchTriangle}{%
+ \tkz@DefIntouchTriangle[]}}
+
+\def\tkz@DefIntouchTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \tkzInCenter(#2)
+ \pgfnodealias{tkz@pt}{tkzPointResult}
+ \@DefIntouchTriangle(#2,#2)(#3,\tkz@stop)
+\endgroup
+}
+\let\tkzDefContactTriangle\tkzDefIntouchTriangle
+%<--------------------------------------------------------------------------–>
+% Extouch Triangle
+% The extouch triangle T_1T_2T_3 is the triangle formed by the points of tangency of a triangle A_1A_2A_3 with its excircles J_1, J_2, and J_3.
+%<--------------------------------------------------------------------------–>
+\def\tkzDefExtouchTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefExtouchTriangle}{%
+ \tkz@DefExtouchTriangle[]}}
+
+\def\tkz@DefExtouchTriangle[#1](#2,#3,#4)#5{%
+\begingroup
+ \SetUpPTTR{#1}
+ \foreach \name [count=\i] in {#5} {%
+ \global\expandafter\edef\csname tkz@point\i\endcsname{\name}
+ }
+ \tkzDefExcentralTriangle(#2,#3,#4){tkz@a,tkz@b,tkz@c}
+ \tkzUProjection(#3,#4)(tkz@a)
+ \pgfnodealias{\tkz@pttr@name\csname tkz@point1\endcsname}{tkzPointResult}
+ \tkzUProjection(#2,#3)(tkz@c)
+ \pgfnodealias{\tkz@pttr@name\csname tkz@point3\endcsname}{tkzPointResult}
+ \tkzUProjection(#2,#4)(tkz@b)
+ \pgfnodealias{\tkz@pttr@name\csname tkz@point2\endcsname}{tkzPointResult}
+\endgroup
+}
+
+%<--------------------------------------------------------------------------–>
+% Feuerbach triangle The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles
+
+\def\tkzDefFeuerbachTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefFeuerbachTriangle}{\tkz@DefFeuerbachTriangle[]}}
+
+\def\tkz@DefFeuerbachTriangle[#1](#2,#3,#4)#5{%
+\begingroup
+ \SetUpPTTR{#1}
+ \foreach \name [count=\i] in {#5} {%
+ \global\expandafter\edef\csname tkz@point\i\endcsname{\name}
+ }
+ \tkzDefExCircle(#2,#3,#4)
+ \pgfnodealias{tkz@b}{tkzPointResult} \tkzGetLength{tkz@rb}
+ \tkzDefExCircle(#3,#4,#2)
+ \pgfnodealias{tkz@c}{tkzPointResult} \tkzGetLength{tkz@rc}
+ \tkzDefExCircle(#4,#2,#3)
+ \pgfnodealias{tkz@a}{tkzPointResult} \tkzGetLength{tkz@ra}
+ \tkzInterLC[R](#3,tkz@b)(tkz@b,\tkz@rb pt)
+ \tkzGetFirstPoint{\tkz@pttr@name\csname tkz@point2\endcsname}
+ \tkzInterLC[R](#4,tkz@c)(tkz@c,\tkz@rc pt)
+ \tkzGetFirstPoint{\tkz@pttr@name\csname tkz@point3\endcsname}
+ \tkzInterLC[R](#2,tkz@a)(tkz@a,\tkz@ra pt)
+ \tkzGetFirstPoint{\tkz@pttr@name\csname tkz@point1\endcsname}
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+% Centroid
+%<--------------------------------------------------------------------------–>
+% The medial triangle or midpoint triangle of a triangle ABC
+\def\@DefCentroidTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \pgfcoordinate{#4}{%
+ \pgfpointscale{0.5}{%
+ \pgfpointadd{\pgfpointanchor{#2}{center}}%
+ {\pgfpointanchor{\tkz@last}{center}}}
+ }%
+ \ifx\tkz@tmp\tkz@stop\else\@DefCentroidTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+ }
+\def\tkzDefCentroidTriangle{\pgfutil@ifnextchar[{\tkz@DefCentroidTriangle}
+ {\tkz@DefCentroidTriangle[]}}
+\def\tkz@DefCentroidTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \@DefCentroidTriangle(#2,#2)(#3,\tkz@stop)
+\endgroup
+}
+\let\tkzDefMedialTriangle\tkzDefCentroidTriangle
+\let\tkzDefMidpointTriangle\tkzDefCentroidTriangle
+%<--------------------------------------------------------------------------–>
+% OrthicTriangle H Ha Hb Hc
+%<--------------------------------------------------------------------------–>
+% Orthic Triangle
+%<--------------------------------------------------------------------------–>
+\def\@DefOrthicTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \tkzUProjection(#2,\tkz@last)(#1)
+ \pgfnodealias{#4}{tkzPointResult}
+ \ifx\tkz@tmp\tkz@stop\else\@DefOrthicTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+}
+
+\def\tkzDefOrthicTriangle{\pgfutil@ifnextchar[{\tkz@DefOrthicTriangle}
+ {\tkz@DefOrthicTriangle[]}}
+\def\tkz@DefOrthicTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \@DefOrthicTriangle(#2,#2)(#3,\tkz@stop)
+\endgroup
+}
+\let\tkzDefAltitudeTriangle\tkzDefOrthicTriangle
+
+%<--------------------------------------------------------------------------–>
+% The Euler triangle of a triangle ABC is the triangle E_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective vertices. The vertices of the triangle are known as the Euler points, and lie on the nine-point circle.
+
+\def\tkzDefEulerTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefEulerTriangle}{\tkz@DefEulerTriangle[]}}
+\def\tkz@DefEulerTriangle[#1](#2,#3,#4)#5{%
+\begingroup
+ \SetUpPTTR{#1}
+ \pgfinterruptboundingbox
+ \tkzOrthoCenter(#2,#3,#4)
+ \pgfnodealias{tkz@e}{tkzPointResult}
+ \tkzDefMidPoint(#2,tkz@e)
+ \pgfnodealias{tkz@m1}{tkzPointResult}
+ \tkzDefMidPoint(#3,tkz@e)
+ \pgfnodealias{tkz@m2}{tkzPointResult}
+ \tkzDefMidPoint(#4,tkz@e)
+ \pgfnodealias{tkz@m3}{tkzPointResult}
+ \endpgfinterruptboundingbox
+ \foreach \name [count=\i] in {#5} {%
+ \coordinate (\tkz@pttr@name\name) at (tkz@m\i);
+ }
+\endgroup
+}
+%<--------------------------------------------------------------------------–>
+%
+%<--------------------------------------------------------------------------–>
+\def\tkzDefTangentialTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefTangentialTriangle}{\tkz@DefTangentialTriangle[]}}
+\def\tkz@DefTangentialTriangle[#1](#2,#3,#4)#5{%
+\begingroup
+ \SetUpPTTR{#1}
+ \tkzCircumCenter(#2,#3,#4)
+ \pgfnodealias{tkz@circ}{tkzPointResult}
+ \tkzDefLine[orthogonal=through #2](tkz@circ,#2)
+ \pgfnodealias{tkz@pta}{tkzPointResult}
+ \tkzDefLine[orthogonal=through #3](tkz@circ,#3)
+ \pgfnodealias{tkz@ptb}{tkzPointResult}
+ \tkzDefLine[orthogonal=through #4](tkz@circ,#4)
+ \pgfnodealias{tkz@ptc}{tkzPointResult}
+ \tkzInterLL(#2,tkz@pta)(#3,tkz@ptb)
+ \pgfnodealias{tkz@tg3}{tkzPointResult}
+ \tkzInterLL(#3,tkz@ptb)(#4,tkz@ptc)
+ \pgfnodealias{tkz@tg1}{tkzPointResult}
+ \tkzInterLL(#4,tkz@ptc)(#2,tkz@pta)
+ \pgfnodealias{tkz@tg2}{tkzPointResult}
+ \foreach \name [count=\i] in {#5} {%
+ \coordinate (\tkz@pttr@name\name) at (tkz@tg\i);
+ }
+\endgroup
+}
+%<--------------------------------------------------------------------------–
+% tkzDefSymmedianLine
+%<--------------------------------------------------------------------------–
+% The Incentral triangle is the triangle whose vertices are determined by
+% theintersections of the reference triangle’s angle bisectors with the
+% respective opposite sides.
+%<--------------------------------------------------------------------------–>
+\def\@DefSymmedianTriangle(#1,#2,#3)(#4,#5){%
+ \def\tkz@tmp{#5}%
+ \tkz@recuplast(#3)
+ \tkzDefSymmedianLine(#2,#1,\tkz@last)
+ \tkzInterLL(#2,\tkz@last)(#1,tkzPointResult)
+ \pgfnodealias{#4}{tkzPointResult}
+ \ifx\tkz@tmp\tkz@stop\else\@DefSymmedianTriangle(#2,#3)(#5)\fi
+ \pgfnodealias{\tkz@pttr@name#4}{#4}
+}
+
+\def\tkzDefSymmedianTriangle{\pgfutil@ifnextchar[{%
+ \tkz@DefSymmedianTriangle}{%
+ \tkz@DefSymmedianTriangle[]}}
+
+\def\tkz@DefSymmedianTriangle[#1](#2)#3{%
+\begingroup
+ \SetUpPTTR{#1}
+ \pgfinterruptboundingbox
+ \@DefSymmedianTriangle(#2,#2)(#3,\tkz@stop)
+ \endpgfinterruptboundingbox
+\endgroup
+}
+
+\makeatother
+\endinput \ No newline at end of file