%% D'apres un fichier original en PSTricks de François Meria.
%% http://melusine.eu.org/syracuse/texpng/cprl/meria/doc92/

%% \psset{unit=0.46cm}
20 setxunit

%% \pspicture(-4,-2.2)(16,14.5)
-4 16 setxrange
-2.2 14.5 setyrange

setTimes  %% selection de la police

%%     \pstGeonode[PointSymbol=none,PosAngle={-135,-45},PointName=none](0,0){B}(12,0){C}            %,PointName=none
/B {0 0} def
/C {12 0} def

%%     \pstRotation[PointSymbol=none,RotAngle=60,PosAngle=90,PointName=none]{B}{C}{A}
C B 60 rotatepoint /A defpoint

%%     \pstMiddleAB[PointSymbol=none,PosAngle=-45,PointName=none]{B}{C}{J}
B C milieu /J defpoint

%%     \pstMiddleAB[PointSymbol=none,PosAngle=45,PointName=none]{A}{C}{K}
A C milieu /K defpoint

%%     \pstMiddleAB[PointSymbol=none,PosAngle=135,PointName=none]{B}{A}{I}
B A milieu /I defpoint

%%     \pstInterLL[PointName=none,PointSymbol=none]{A}{J}{B}{K}{O}
A J B K interdroite /O defpoint

%%     \pstInterLC[Radius=\pstDistVal{2},PointName=none,PointSymbol=none,PosAngle=-90]{A}{O}{J}{}{Z_3}{D}
%%     \pstInterLC[Radius=\pstDistVal{2},PointName=none,PointSymbol=none,PosAngle=135]{C}{O}{I}{}{Z_1}{E}
%%     \pstInterLC[Radius=\pstDistVal{2},PointName=none,PointSymbol=none,PosAngle=45]{B}{O}{K}{}{Z_2}{F}

%% je n'ai pas compris. tant pis, on definit D, E, F avec une homothetie
1.15 C I ABpoint /E defpoint
1.15 B K ABpoint /F defpoint
1.15 A J ABpoint /D defpoint

%%     \pstTranslation[PointName=none,PointSymbol=none]{I}{E}{A}{t}
%%     \pstTranslation[PointName=none,PointSymbol=none]{K}{F}{A}{p}
%%     \pstTranslation[PointName=none,PointSymbol=none]{J}{D}{B}{q}
%%     \pstInterLL[PointName=none,PointSymbol=none]{D}{q}{E}{t}{B'}
%%     \pstInterLL[PointName=none,PointSymbol=none]{D}{q}{p}{F}{C'}
%%     \pstInterLL[PointName=none,PointSymbol=none]{F}{p}{E}{t}{A'}

%% on ne fait pas pareil : on definit les droites d1, d2, d3, cotes du
%% triangle

C I E perp /d1 defdroite  %% prependiculaire a (CI) passant par E
A J D perp /d2 defdroite
B K F perp /d3 defdroite

%% les points A', B' et C' sont les intersections de ces droites
d1 d2 interdroite /B' defpoint
d3 d2 interdroite /C' defpoint
d1 d3 interdroite /A' defpoint

1.5 setlinewidth
2 setlinejoin
%%     \pspolygon[linewidth=1.5pt](A')(B')(C') %[fillstyle=solid,fillcolor=yellow]
/fillstyle {jaune fill} def
[A' B' C'] polygone*

/cheminAC {
   A smoveto
   K A C arcp_   %% sens trigo
   F C A arcnp_  %% sens trigo inverse 
} def

%% remplissage des zones en bleu
gsave 
newpath
   cheminAC
   clip
   bleu fill
grestore

/cheminBC {
   C smoveto
   J C B arcp_   %% sens trigo
   D B C arcnp_  %% sens trigo inverse 
} def

gsave 
newpath
   cheminBC
   clip
   bleu fill
grestore

/cheminBA {
   B smoveto
   I B A arcp_   %% sens trigo
   E A B arcnp_  %% sens trigo inverse 
} def

gsave 
newpath
   cheminBA
   clip
   bleu fill
grestore

%% remplissage des zones en blanc
gsave
   newpath
      cheminAC
   clip
   newpath
      cheminBC
   clip
   blanc fill
grestore

gsave
   newpath
      cheminAC
   clip
   newpath
      cheminBA
   clip
   blanc fill
grestore

gsave
   newpath
      cheminBC
   clip
   newpath
      cheminBA
   clip
   blanc fill
grestore

%%     \pstArcOAB[linewidth=1.5pt]{I}{B}{A}
%%     \pstArcOAB[linewidth=1.5pt]{E}{B}{A}
%%     \pstArcOAB[linewidth=1.5pt]{K}{A}{C}
%%     \pstArcOAB[linewidth=1.5pt]{F}{A}{C}
%%     \pstArcOAB[linewidth=1.5pt]{J}{C}{B}
%%     \pstArcOAB[linewidth=1.5pt]{D}{C}{B}

%% trace des arcs de cercles
I B A arcp
E B A arcp
K A C arcp
F A C arcp
J C B arcp
D C B arcp

%%     \put(5,-3.8){Figure $2$}
%% \endpspicture

%% on affiche le nom des points
(B') B' dltext   (B) B dltext
(C') C' drtext	 (C) C drtext
(A') A' uctext	 (A) A uctext
(J) J dctext     (E) E ultext
(K) K urtext	 (F) F urtext
(I) I ultext	 (D) D dctext