input geometriepoint; beginfig(1);%dm2 u=1cm; z0=u*(1,1);label.llft(btex $B$ etex,z0);affixe.B(z0); z1=u*(6,1);label.lrt(btex $C$ etex,z1);affixe.C(z1); z2=u*(5,5);label.top(btex $A$ etex,z2);affixe.A(z2); draw z0--z1--z2--cycle; affixe.H(projet(A,B,C)); draw z2--z.H; label.bot(btex $H$ etex,z.H); label.bot(btex $M$ etex,1/2[z0,z1]); draw z2--1/2[z0,z1]; draw codeperp(A,H,B,5); endfig; beginfig(2);%dm2 affixe.O(u*(1,1));label.llft(btex $O$ etex,z.O); affixe.T(u*(6,1));label.lrt(btex $T$ etex,z.T); path cerc; cerc=cercledia(O,T); affixe.S(point(0.35*length cerc) of cerc);label.top(btex $S$ etex,z.S); draw z.S--z.O--z.T--cycle; draw codeperp(O,S,T,5); affixe.L(3/5[z.T,z.S]);label.top(btex $L$ etex,z.L); affixe.U(3/5[z.T,z.O]);label.bot(btex $U$ etex,z.U); draw z.L--z.U; draw codeperp(U,L,T,5); endfig; beginfig(3); u:=0.5cm; affixe.T(u*(1,1))o; affixe.M(u*(7,5))o; draw droite(T,M,1.25); affixe.P(1/5[z.T,z.M])e; affixe.S(u*(0.5,7))so; affixe.N(u*(7,2))ne; draw droite(S,N,1.25); affixe.I((z.S--z.N) intersectionpoint (z.T--z.M))n; draw droite(S,T,1.25); draw para(P,T,S,1.2); affixe.R(para(P,T,S,1.2) intersectionpoint (z.S--z.N))ne; draw droite(M,N,1.25); endfig; beginfig(4);%dm6 z0=(0,0);dotlabel.lft(btex $B$ etex,z0); z1=(5cm,0); z2=1/5[z0,z1]; z3=2/3[z0,z1];dotlabel.bot(btex $C$ etex,z3); z4=1/2[z0,z3];dotlabel.bot(btex $I$ etex,z4); z5=(1.2cm,5cm);dotlabel.top(btex $D$ etex,z5); z6=1/4[z2,z5];dotlabel.ulft(btex $A$ etex,z6); draw z0--z3--z5--cycle; draw z4--z5; draw z6--z0 dashed evenly; draw z6--z5 dashed evenly; draw z6--z4 dashed evenly; draw z6--z3 dashed evenly; endfig; beginfig(5);%dm8 unit=0.5*cm; z0=(1*unit,1*unit);label.llft(btex $A$ etex,z0); z1=z0 shifted (6*unit,0);label.lrt(btex $B$ etex,z1); z3=z0 shifted (3*unit,2*unit);label.lft(btex $D$ etex,z3); z4=z0 shifted (0,6*unit);label.ulft(btex $E$ etex,z4); z5=z4 shifted (6*unit,0);label.top(btex $F$ etex,z5); z2=z1 shifted (3*unit,2*unit);label.rt(btex $C$ etex,z2); z6=z5 shifted (3*unit,2*unit);label.urt(btex $G$ etex,z6); z7=z4 shifted (3*unit,2*unit);label.top(btex $H$ etex,z7); draw z0--z1--z2--z6--z7--z4--cycle; draw z4--z5--z6;draw z5--z1--z6; draw z7--z3--z0 dashed evenly; draw z6--z3--z1 dashed evenly; draw z2--z3 dashed evenly; z8=3/5[z6,z2];label.rt(btex $J$ etex,z8); z9=3/5[z6,z1];label.lrt(btex $K$ etex,z9); z10=3/5[z6,z3];label.ulft(btex $L$ etex,z10); draw z8--z9; draw z8--z10--z9 dashed evenly; clip currentpicture to (0,0)--(11*unit,0)--(11*unit,11*unit)--(0,11*unit)--cycle; endfig; beginfig(6);%dm9 z0=(1*unit,1*unit);label.bot(btex $C$ etex,z0); z1=(8*unit,1*unit);label.bot(btex $D$ etex,z1); z2=(9*unit,7*unit);label.top(btex $B$ etex,z2); z3=(5*unit,7*unit);label.top(btex $A$ etex,z3); z4=(z1--z3) intersectionpoint (z0--z2); label.rt(btex $O$ etex,z4); draw z3--z2--z0--z1; draw z3--z1 dashed evenly; clip currentpicture to (0,0)--(10*unit,0)--(10*unit,8*unit)--(0,8*unit)--cycle; endfig; beginfig(7);%dm14 pair p[]; p0=u*(1,2);label.llft(btex $E$ etex,p0); p1=u*(7,1.5);label.lrt(btex $F$ etex,p1); p3=u*(2,3.5);label.urt(btex $H$ etex,p3); p7=u*(1,7);label.ulft(btex $A$ etex,p7); p2=p1 shifted (p3-p0);label.rt(btex $G$ etex,p2); p4=p1 shifted (p7-p0);label.lrt(btex $B$ etex,p4); p5=p4 shifted (p3-p0);label.urt(btex $C$ etex,p5); p6=p7 shifted (p3-p0);label.top(btex $D$ etex,p6); draw p7--p0--p1--p2--p5--p6--p7--p4--p1; draw p5--p4; draw p0--p3--p6 dashed evenly; draw p3--p2 dashed evenly; p8=3.5/5[p6,p3];dotlabel.rt(btex $I$ etex,p8); draw p0--p6--p2 dashed evenly; draw p6--p1 dashed evenly; endfig; end