input latexmp; setupLaTeXMP(class="article",options="12pt",fontencoding="T1",inputencoding="latin1",language="frenchb",packages="fourier,textpathmp"); input textpath; prologues:=2; input geometriesyr16; figure(-10u,-10u,10u,10u); pair F,F',O,K,A,A',B,B',P[],Q[],M[],N[]; F=u*(-4.5,0); F'=u*(4.5,0); O=iso(F,F'); path cc; cc=cercledia(F,F'); K-F=u*(0,5); A=cercles(O,K) intersectionpoint droite(F,F'); A'=symetrie(A,O); B=cercles(F,5u) intersectionpoint cercles(F',5u); B'=symetrie(B,F,F'); for k=1 step 2 until 359: P[k]=pointarc(cc,k); Q[k]=symetrie(P[k],O,projection(O,A,P[k])); M[k]=cercles(F,abs(A-P[k])) intersectionpoint cercles(F',abs(A-Q[k])); N[k]=symetrie(M[k],F,F'); endfor; drawoptions(dashed evenly withcolor gris); trace cc; drawoptions(withcolor rouge); path ovaledecasini; ovaledecasini=M1 for k=3 step 2 until 359: --M[k] endfor for k=359 step -2 until 1: --N[k] endfor --cycle; trace ovaledecasini; drawoptions(withcolor bleu); trace textpath("\Large Ovale de Casini",ovaledecasini,0); fin; end