verbatimtex
%&latex
\documentclass{article}
\usepackage[frenchb]{babel}
\begin{document}
etex

input geometriesyr13;
figure(-5u,-5u,5u,5u);
z0=(0,0);label.lft(btex $O$ etex,z0);
z1=(3u,-2u);
draw z0--z1;
z2=point 0.85*(length(z0--z1))of (z0--z1);label.llft(btex $M$ etex,z2);
draw (z2 shifted (-u/20,u/20))--(z2 shifted (u/20,-u/20)) withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,-u/20))--(z2 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
z3 = z1 rotated 140;z4 = z2 rotated 140;draw z0--z3;label.rt(btex $x$ etex,z3);
draw (z4 shifted (-u/20,u/20))--(z4 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z4 shifted (-u/20,-u/20))--(z4 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
label.lft(btex $M'$ etex,z4);
path c,d;
c:=fullcircle scaled (2*(abs(z2)));
d= c cutbefore (z0--z1)cutafter (z0--z3);
ahlength:=6bp;
draw (c cutbefore (z0--z1) ) dashed evenly;
drawarrow (c cutafter (z0--z3))dashed evenly;
draw marqueangle(z2,z0,z4,0);label.urt(btex 140\degres etex,w);
draw codesegments(z0,z2,z0,z4,2);
fin;
figure(-5u,-5u,5u,5u);%n°2
z0=(0,0)*u;label.lft(btex$O$etex,z0);
z1=(3.5u,2.5u);
draw z0--z1;
z2= point 0.85*(length(z0--z1))of (z0--z1);label.top(btex$M$etex,z2);
draw (z2 shifted (-u/20,u/20))--(z2 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,-u/20))--(z2 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
z3 = z1 rotated -60;z4 = z2 rotated -60;draw z0--z3;label.llft(btex$x$etex,z3);
draw (z4 shifted (-u/20,u/20))--(z4 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z4 shifted (-u/20,-u/20))--(z4 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
label.llft(btex$M'$etex,z4);
path c, d;
c:=fullcircle scaled (2*(abs(z2)));
d= c cutbefore (z0--z1)cutafter (z0--z3);
ahlength:=6bp;
drawarrow (reverse(c cutbefore (z0--z3))) dashed evenly;
draw(c cutafter (z0--z1))dashed evenly;
draw marqueangle(z4,z0,z2,0);label.urt(btex 60\degres etex,w);
draw codesegments(z0,z2,z0,z4,2);
fin;
figure(-5u,-5u,5u,5u);%n°3
z0=(0,0)*u;dotlabel.bot(btex$O$etex,z0);
z1=(2u,0);label.bot(btex$M$etex,z1);
z2=z1 rotated 180; draw z1--z2;label.bot(btex$M'$etex,z2);
draw (z1 shifted (-u/20,u/20))--(z1 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z1 shifted (-u/20,-u/20))--(z1 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,u/20))--(z2 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,-u/20))--(z2 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
path c; c=fullcircle scaled (2*(abs(z1)));
drawarrow (c cutafter (z0--z2)) dashed evenly;
label.top(btex 180\degres etex,z0 shifted(0,0.4u));
draw codesegments(z0,z1,z0,z2,2);
fin;
figure(-10u,-10u,10u,10u);%N°4
z0=(0,0)*u;label.bot(btex$O$etex,z0);
z1=(3u,4u);label.bot(btex$I$etex,z1);
transform r;
r = identity rotated 110;
draw (z0 shifted (-u/20,u/20))--(z0 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z0 shifted (-u/20,-u/20))--(z0 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
draw (z1 shifted (-u/20,u/20))--(z1 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z1 shifted (-u/20,-u/20))--(z1 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
path c,d;c=fullcircle scaled 4u shifted z1; d = c transformed r;
draw c;draw d;
z2=z1 transformed r;label.rt(btex$I'$etex,z2);
draw (z2 shifted (-u/20,u/20))--(z2 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,-u/20))--(z2 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
z3= point 0 of c;label.rt(btex$B$etex,z3);
z4= point 0.5*(length c) of c;label.lft(btex$A$etex,z4);
z5=z3 transformed r;label.top(btex$B'$etex,z5);
z6= z4 transformed r;label.bot(btex$A'$etex,z6);
z7= point 0.2*(length c) of c ;label.urt(btex$C$etex,z7);
z8= z7 transformed r;label.ulft(btex$C'$etex,z8);
draw z3--z4--z7--cycle;draw z5--z6--z8--cycle;
z9=0.5[z4,z7];label.top(btex$K$etex,z9);
z10=z9 transformed r;label.llft(btex$K'$etex,z10);
draw z1--z9;draw z2--z10;draw codeperp(z3,z7,z4,8);draw codeperp(z1,z9,z4,8);
draw codeperp(z5,z8,z10,8);draw codeperp(z2,z10,z6,8);
label.top(btex$r$etex,0.5[z1,z3]);label.lft(btex$r$etex,0.5[z2,z5]);
label.top(btex$\cal{F}$etex,point 0.3*(length c) of c);
label.bot(btex$\cal{F}'$etex,point 0.4*(length d) of d);
path e,f,g;e=fullcircle scaled (2*abs(z1));
f=fullcircle scaled (2*abs(z4));g=fullcircle scaled (2*abs(z7));
drawarrow (e cutbefore (z1--z4) cutafter (z2--z6)) dashed evenly;
drawarrow (f cutbefore (z1--z4) cutafter (z2--z6 + 0.5(z6-z2))) dashed evenly;
drawarrow (g cutbefore (z4--z7) cutafter (z6--z8)) dashed evenly;
draw z0--z1 dashed evenly;draw z0--z2 dashed evenly;draw z0--z4 dashed evenly;draw z0--z6 dashed evenly;
draw marqueangle(z1,z0,z2,0);label.top(btex 100\degres etex,w);
draw z0--z7 dashed evenly;draw z0--z8 dashed evenly;
z11= point 0.28*(length g) of g shifted (0,1u);
drawarrow z11 shifted (0.5u,-0.2u)..z11..z11 shifted (-0.5u,-0.2u);label.top(btex {\textbf{\Large{+}}}etex,z11);
fin;
figure(-5u,-5u,5u,5u);%N°5
z0=(0,0)*u;dotlabel.llft(btex$O$etex,z0);
z1=(2u,0);label.bot(btex$M$etex,z1);
z2=z1 rotated 90; draw z1--z0--z2;label.ulft(btex$M'$etex,z2);
draw (z1 shifted (-u/20,u/20))--(z1 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z1 shifted (-u/20,-u/20))--(z1 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,u/20))--(z2 shifted (u/20,-u/20))withpen pencircle scaled 1 bp;
draw (z2 shifted (-u/20,-u/20))--(z2 shifted (u/20,u/20))withpen pencircle scaled 1 bp;
path c; c=fullcircle scaled (2*(abs(z1)));
drawarrow (c cutafter (z0--z2)) dashed evenly;
label.top(btex 90\degres etex,z0 shifted(0.5u,0.4u));
draw codeperp(z1,z0,z2,8);
draw codesegments(z0,z1,z0,z2,2);
fin;
end