verbatimtex
%&latex
\documentclass{article}
\usepackage{mathrsfs}
\begin{document}
etex

input geometriesyr16;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,R,S,T;
A=u*(5,3.5);
B=u*(9,1.5);
R=u*(2,1);
S=u*(3,4);
T=u*(6,0.5);
trace triangle(R,S,T);
trace droite(A,B);
label.top(btex $(d)$ etex,6/5[A,B]);
label(btex $\mathscr F$ etex,iso(R,S,T));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair C,D,R,S,T,U;
C=u*(1,3);
D=u*(7,5);
R=u*(4,1);
S=u*(6,1);
T=u*(8,4);
U=u*(4,3);
trace codeperp(U,R,S,5);
trace R--S--T--U--cycle;
label(btex $\mathscr F$ etex,iso(R,S,T,U));
label.top(btex $(d)$ etex,6/5[C,D]);
trace droite(C,D);
fin;

figure(u,0,10u,8u);
draw feuillet;
pair O,E,F;
O=u*(4,1);
path cc,cd;
cc=cercle(O,2.5cm);
cd=(point(0) of cc)--(subpath(0,length cc/2) of cc)--cycle;
E=u*(3,7);
F=u*(5,4);
marque_p:="croix";
MarquePoint(O);
trace cd;
trace droite(E,F);
label.urt(btex $(d)$ etex,6/5[F,E]);
label(btex $\mathscr F$ etex,O shifted(u*(0,0.5)));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F,K,L;
K=u*(9,7);
L=u*(6,5);
A=u*(5,3);
B-A=u*(0,2);
C-B=u*(3,1);
D-C=u*(0,-4);
E-D=u*(-2,0);
F-E=u*(0,1);
MarquePoint(iso(E,F));
path ce;
ce=A--B--C--D--E--arccercle(E,F,iso(E,F))--cycle;
trace ce;
trace droite(K,L);
label.ulft(btex $(d)$ etex,2[K,L]);
label(btex $\mathscr F$ etex,iso(A,B,C,D,E,F));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F;
A=u*(3,1);
B=u*(2,2);
C=B shifted(u*(0,2));
D-C=u*(3,1);
E-D=u*(0,1);
F-E=u*(1.5,0);
path cc;
cc=A--B--C--D--E--F;
trace cc;
trace droite(A,F);
label.ulft(btex $(d)$ etex,5.5/5[F,A]);
label(btex $\mathscr F$ etex,iso(A,B,C,D,E,F));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F,G,H,I;
A=u*(7,1);
B-A=u*(-4,0);
C-B=u*(0,2);
D-C=u*(-1,0);
E-D=u*(0,2);
F-E=u*(1,0);
G-F=u*(0,1);
H-G=u*(2,0);
I=F shifted(u*(1,-1));
path cc;
cc=A--B--C--D--E--F--G--H;
draw cercle(I,1u);
MarquePoint(I);
trace cc;
trace droite(A,H);
label.ulft(btex $(d)$ etex,6/5[H,A]);
label(btex $\mathscr F$ etex,iso(A,B,H));
fin;

%correction
figure(u,0,10u,8u);
draw feuillet;
pair A,B,R,S,T;
A=u*(5,3.5);
B=u*(9,1.5);
R=u*(2,1);
S=u*(3,4);
T=u*(6,0.5);
trace triangle(R,S,T) dashed evenly;
trace symetrie(triangle(R,S,T),A,B);
trace droite(A,B);
label.top(btex $(d)$ etex,6/5[A,B]);
label(btex $\mathscr F$ etex,iso(R,S,T));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair C,D,R,S,T,U;
C=u*(1,3);
D=u*(7,5);
R=u*(4,1);
S=u*(6,1);
T=u*(8,4);
U=u*(4,3);
trace codeperp(U,R,S,5);
trace R--S--T--U--cycle dashed evenly;
trace symetrie((R--S--T--U--cycle),D,C);
label(btex $\mathscr F$ etex,iso(R,S,T,U));
label.top(btex $(d)$ etex,6/5[C,D]);
trace droite(C,D);
fin;

figure(u,0,10u,8u);
draw feuillet;
pair O,E,F;
O=u*(4,1);
path cc,cd;
cc=cercle(O,2.5cm);
cd=(point(0) of cc)--(subpath(0,length cc/2) of cc)--cycle;
E=u*(3,7);
F=u*(5,4);
marque_p:="croix";
MarquePoint(O);
trace cd dashed evenly;
trace symetrie(cd,F,E);
trace droite(E,F);
label.urt(btex $(d)$ etex,6/5[F,E]);
label(btex $\mathscr F$ etex,O shifted(u*(0,0.5)));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F,K,L;
K=u*(9,7);
L=u*(6,5);
A=u*(5,3);
B-A=u*(0,2);
C-B=u*(3,1);
D-C=u*(0,-4);
E-D=u*(-2,0);
F-E=u*(0,1);
MarquePoint(iso(E,F));
path ce;
ce=A--B--C--D--E--arccercle(E,F,iso(E,F))--cycle;
trace ce dashed evenly;
trace symetrie(ce,L,K);
trace droite(K,L);
label.ulft(btex $(d)$ etex,2[K,L]);
label(btex $\mathscr F$ etex,iso(A,B,C,D,E,F));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F;
A=u*(3,1);
B=u*(2,2);
C=B shifted(u*(0,2));
D-C=u*(3,1);
E-D=u*(0,1);
F-E=u*(1.5,0);
path cc;
cc=A--B--C--D--E--F;
trace cc dashed evenly;
trace symetrie(cc,A,F);
trace droite(A,F);
label.ulft(btex $(d)$ etex,5.5/5[F,A]);
label(btex $\mathscr F$ etex,iso(A,B,C,D,E,F));
fin;

figure(u,0,10u,8u);
draw feuillet;
pair A,B,C,D,E,F,G,H,I;
A=u*(7,1);
B-A=u*(-4,0);
C-B=u*(0,2);
D-C=u*(-1,0);
E-D=u*(0,2);
F-E=u*(1,0);
G-F=u*(0,1);
H-G=u*(2,0);
I=F shifted(u*(1,-1));
path cc;
cc=A--B--C--D--E--F--G--H;
trace cercle(I,1u) dashed evenly;
trace symetrie(cercle(I,1u),A,H);
MarquePoint(I);
trace cc dashed evenly;
trace symetrie(cc,A,H);
trace droite(A,H);
label.ulft(btex $(d)$ etex,6/5[H,A]);
label(btex $\mathscr F$ etex,iso(A,B,H));
fin;

end