input constantes;
input geometriepoint;
beginfig(1);
  affixe.A(u*(1,1));
  affixe.B(u*(7,1));
  affixe.O(1/2[z.A,z.B]);
  affixe.X((0,0));
  path cc,cd,ce,cf;
  cd=cercle(X,3cm);
  cc=cd yscaled 0.4;
  ce=(subpath(0,0.5*length cc) of cc) shifted z.O;
  label.llft(btex $A$ etex,z.A);
  label.lrt(btex $B$ etex,z.B);
  affixe.M(point(0.3*length ce) of ce);
  label.urt(btex $M$ etex,z.M);
  draw z.B--z.M--z.A dashed evenly;
  draw z.A--z.B;
  affixe.H(projet(M,A,B) shifted (1/10*(z.A-z.B)));
  draw codeperp(M,H,A,5);
  draw z.M--z.H dashed evenly;
  affixe.S(z.M shifted (u*(0,4)));
  draw z.A--z.S--z.B;
  draw z.S--z.M dashed evenly;
  draw codeperp(S,M,A,5);
  label.top(btex $S$ etex,z.S);
  label.bot(btex $H$ etex,z.H);
  affixe.N((z.S--z.A) intersectionpoint ce);
  z.L=z.X shifted (xpart(z.N-z.O),0);
  z.K=cd intersectionpoint perpen(L,A,B,10);
  cf=((subpath(0,(angle(z.K-z.X)*(length cd))/360) of cd) yscaled 0.4) shifted z.O;
  draw cf dashed evenly;
  draw ((subpath((angle(z.K-z.X)*(length cd))/360,(length cd)/2) of cd) yscaled 0.4) shifted z.O;
endfig;
end