input geometriesyr16; u:=7mm; figure(0,2u,8u,8.5u); pair O,M,N,M',N',I,J; O=u*(5,5); path cc; cc=cercles(O,2.5u); M=u*(1,4); N=u*(6,6.5); I=demidroite(O,M) intersectionpoint cc; J=demidroite(O,N) intersectionpoint cc; M'=symetrie(M,I); N'=symetrie(N,J); marque_p:="creux"; pointe(M,N,I,J,M',N',O); trace cc withpen pencircle scaled1.25bp; trace demidroite(O,M) dashed evenly; trace demidroite(O,N) dashed evenly; marque_p:="non"; nomme.lrt(O); nomme.bot(M); nomme.ulft(N); nomme.bot(M'); nomme.ulft(N'); nomme.llft(I); nomme.top(J); fin; u:=8mm; figure(-2u,0,8u,8u); pair O,M[],I[],N[],A,B; O=u*(5,5); path cc; cc=cercles(O,3u); A=u*(2.5,1); B=pointarc(cercles(A,7u),110); trace cc; marque_p:="croix"; nomme.lrt(O); marque_p:="non"; trace segment(A,B); trace marquesegment(A,B); for k=1 upto 10: M[k]=((k-1)/9)[A,B]; I[k]=demidroite(O,M[k]) intersectionpoint cc; N[k]=symetrie(M[k],I[k]); endfor; for k=1 step 2 until 9: trace marquesegment(M[k],M[k+1]); endfor; label(btex M$_1$ etex rotated(angle(B-A)),M1+5mm*(unitvector(B-A) rotated 90)); label(btex M$_2$ etex rotated(angle(B-A)),M2+5mm*(unitvector(B-A) rotated 90)); label(btex M$_3$ etex rotated(angle(B-A)),M3+5mm*(unitvector(B-A) rotated 90)); label(btex M$_4$ etex rotated(angle(B-A)),M4+5mm*(unitvector(B-A) rotated 90)); label(btex M$_5$ etex rotated(angle(B-A)),M5+5mm*(unitvector(B-A) rotated 90)); label(btex M$_6$ etex rotated(angle(B-A)),M6+5mm*(unitvector(B-A) rotated 90)); label(btex M$_7$ etex rotated(angle(B-A)),M7+5mm*(unitvector(B-A) rotated 90)); label(btex M$_8$ etex rotated(angle(B-A)),M8+5mm*(unitvector(B-A) rotated 90)); label(btex M$_9$ etex rotated(angle(B-A)),M9+5mm*(unitvector(B-A) rotated 90)); label(btex M$_{10}$ etex rotated(angle(B-A)),M10+5mm*(unitvector(B-A) rotated 90)); fin; figure(-5u,-7u,8.5u,8.5u); pair O,M[],I[],N[],A,B; O=u*(5,5); path cc,cd; cc=cercles(O,3u); A=u*(2.5,1); cd=cercles(A,4u); trace cc; marque_p:="croix"; nomme.lrt(O); nomme.lrt(A); marque_p:="non"; trace cd dashed evenly; for k=1 upto 10: M[k]=pointarc(cd,k*36); I[k]=demidroite(O,M[k]) intersectionpoint cc; N[k]=symetrie(M[k],I[k]); endfor; for k=1 step 2 until 9: trace marquesegment(M[k],M[k+1]); endfor; label(btex M$_1$ etex rotated(angle(M1-A)),M1+5mm*(unitvector(M1-A))); label(btex M$_2$ etex rotated(angle(M2-A)),M2+5mm*(unitvector(M2-A))); label(btex M$_3$ etex rotated(angle(M3-A)),M3+5mm*(unitvector(M3-A))); label(btex M$_4$ etex rotated(angle(M4-A)),M4+5mm*(unitvector(M4-A))); label(btex M$_5$ etex rotated(angle(M5-A)),M5+5mm*(unitvector(M5-A))); label(btex M$_6$ etex rotated(angle(M6-A)),M6+5mm*(unitvector(M6-A))); label(btex M$_7$ etex rotated(angle(M7-A)),M7+5mm*(unitvector(M7-A))); label(btex M$_8$ etex rotated(angle(M8-A)),M8+5mm*(unitvector(M8-A))); label(btex M$_9$ etex rotated(angle(M9-A)),M9+5mm*(unitvector(M9-A))); label(btex M$_{10}$ etex rotated(angle(M10-A)),M10+5mm*(unitvector(M10-A))); fin; end