input constantes;
input geometriepoint;
beginfig(1);
unit=0.5*cm;
z0=(0,0);label.bot(btex $O$ etex,z0);%centre de la sphère
z1=(0,2.5*unit);label.lft(btex $H$ etex,z1);%centre de la section
path cc;%cercle pour l'ellipse
cc=fullcircle scaled (2*(4+-+2.5)*unit);
path cd;%ellipse
cd=cc yscaled 0.15 shifted z1;
numeric a;%longueur de l'ellipse
a=length cd;
draw subpath(0,(a/2)) of cd dashed evenly;
draw subpath((a/2),a) of cd;
draw fullcircle scaled (8*unit);
z2=point (9*a/10) of cd;label.lrt(btex $A$ etex,z2);
label.llft(btex $({\cal C})$ etex,point (3*a/5) of cd);
draw z0--z1--z2--cycle dashed evenly;
endfig;
beginfig(2);
    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;
end