input geometriesyr12; beginfig(2); pair A,B,C,D,E; A=u*(4,1); C=u*(0,5); D=A rotatedabout(C,40); E=projection(C,A,D); B=1/2[C,E]; draw A--B--C--D--cycle; draw B--E; draw codesegments(A,B,B,C,2); draw codesegments(A,B,B,E,2); draw codesegments(A,E,E,D,1); label.bot(btex $A$ etex,A); label.bot(btex $C$ etex,C); label.lrt(btex $E$ etex,E); label.llft(btex $B$ etex,B); label.top(btex $D$ etex,D); endfig; beginfig(3); z0=u*(1,1);label.llft(btex $A$ etex,z0); pair A,B,C,D,E; A=z0; z1=u*(2.5,1);label.lrt(btex $B$ etex,z1); B=z1; draw (z1 shifted (u*(0,.2)))--(z1 shifted (u*(0,-.2))); draw ((z1 shifted (u*(0,.2)))--(z1 shifted (u*(0,-.2)))) shifted (z1-z0); draw ((z1 shifted (u*(0,.2)))--(z1 shifted (u*(0,-.2)))) shifted (2*(z1-z0)); z2=z1 shifted (z1-z0);C=z2; z3=z2 shifted (z1-z0);D=z3; z4=z3 shifted (z1-z0);E=z4; draw z0--z4; draw codesegments(A,B,B,C,2); draw codesegments(C,D,D,E,2); path cc,cd,ce; cc=cercles(B,abs(z1-z0)); draw subpath(0,(length cc)/2) of cc; cd=cercles(D,abs(z3-z4)); draw subpath((length cd)/2, length cd) of cd; ce=cercles(C,abs(z2-z0)); draw subpath(0,(length ce)/2) of ce; endfig; pair p[]; p0=u*(1,1); p1=u*(7,1); p2=u*(7,4); p3=u*(1,4); p4=(p0--p2) intersectionpoint (p1--p3); p5=1/2[p2,p3]; p6=p4 reflectedabout(p2,p3); beginfig(101); pair M,I,N,E,L,K,O; label.llft(btex $M$ etex,p0);M=p0; label.lrt(btex $I$ etex,p1);I=p1; label.urt(btex $N$ etex,p2);N=p2; label.ulft(btex $E$ etex,p3);E=p3; label.bot(btex $L$ etex,p4);L=p4; label.urt(btex $K$ etex,p5);K=p5; label.top(btex $O$ etex,p6);O=p6; draw p0--p1--p2--p3--cycle; draw codeperp(M,I,N,5); draw codeperp(I,N,E,5); draw codeperp(N,E,M,5); draw p0--p2;draw p1--p3; draw p4--p6; draw codesegments(L,K,K,O,2); draw codeperp(L,K,E,5); draw p2--p6--p3; endfig; beginfig(102); pair W,Y,X; p10=u*(5,5);W=p10; p11=u*(8,5); path cc,cd,ce,cf; cc=cercles(W,abs(p11-p10)); draw cc; drawdblarrow p10--(point((length cc)/2) of cc); Y=1/2[p10,point((length cc)/2) of cc]; label.top(btex 2~cm etex,Y); cd=cercles(Y,abs(p10-Y)); X=1/2[p10,p11]; ce=cercles(X,abs(p10-X)); cf=(subpath(0,(length ce)/2) of ce)--(subpath(length cd,(length cd)/2) of cd)--(subpath((length cc)/2,length cc) of cc)--cycle; fill cf withcolor 0.1[white,black]; draw cf; endfig; end