input latexmp;
setupLaTeXMP(class="article",options="12pt",fontencoding="T1",inputencoding="latin1",language="frenchb",packages="fourier,textpathmp");
input textpath;

prologues:=2;

input geometriesyr16;

figure(-5u,-5u,12.5u,7u);
pair A,O,E,C,D,P[],M[],N[],B[];
O=u*(5,0);
A-O=u*(3,2);
E=symetrie(A,O);
C-O=u*(-2,1);
D=symetrie(C,O);
path dd,de,d';
dd=droite(C,D);
d'=droite(A,E);
de=parallele(C,D,A);
n=0;
marque_p:="plein";
for k=angle(A-O) step 1 until (180+angle(A-O)):
  P[k]=pointarc(cercles(O,5u),k);
  if (droite(O,P[k]) intersectiontimes de)<>(-1,-1):
    B[k]=droite(O,P[k]) intersectionpoint de;
    n:=n+1;
    M[n]=cercles(O,abs(A-B[k])) intersectionpoint demidroite(O,P[k]);
    N[n]=symetrie(M[n],O);
  fi;
endfor;
drawoptions(dashed evenly withcolor gris);
trace dd;
trace d';
trace de;
drawoptions(withcolor rouge);
path Cappa[];
Cappa1=M1
for k=2 upto n:
  --M[k]
endfor;
Cappa2=N1
for k=2 upto n:
  --N[k]
endfor;
trace Cappa1;
trace Cappa2;
drawoptions(withcolor bleu);
trace textpath("\Large Cappa",reverse(Cappa1),0.9);
fin;

end