% --- start of displayed preamble in the book --- % --- end of displayed preamble in the book --- def NinepointsLabelsAndDots= pickup pencircle scaled 2pt; drawdot(A);drawdot(B);drawdot(C); drawdot(D);drawdot(E);drawdot(F); drawdot(G);drawdot(H);drawdot(I); drawdot(X);drawdot(J);drawdot(K); drawdot(L);drawdot(N); pickup pencircle scaled .5; label.lrt(btex \$A\$ etex,A); label.urt(btex \$B\$ etex,B); label.lft(btex \$C\$ etex,C); label.rt(btex \$D\$ etex,D); label.ulft(btex \$E\$ etex,E); label.llft(btex \$F\$ etex,F); label.ulft(btex \$G\$ etex,G); label.bot(btex \$H\$ etex,H); label.lrt(btex \$I\$ etex,I); label.urt(btex \strut\$X\$ etex,X); label.bot(btex \$J\$ etex,J); label.llft(btex \strut\$K\$ etex,K); label.urt(btex \$L\$ etex,L); label.lft(btex \$N\$ etex,N); enddef; defaultfont:="ptmr8r"; warningcheck:=0; beginfig(1) numeric u;u=1cm; pair A,B,C,D,E,F,G,H,I,J,K,L,N,X; A=origin;B-A=(0,5u);C-A=(-7u,u); % A,B,C D-A=B-D;E-B=C-E;F-A=C-F; % middles D,E,F % then, the three heights: G=whatever[B,C]=whatever[A,A+((C-B) rotated 90)]; % G H=whatever[A,C]=whatever[B,B+((C-A) rotated 90)]; % H I=whatever[A,B]=whatever[C,C+((B-A) rotated 90)]; % I % then, the orthocenter X X=(A--G) intersectionpoint (C--I); % and the middles J, K and L of AX, BX and CX J=.5[A,X];K=.5[B,X];L=.5[C,X]; % the center of the nine points circle N=whatever[.5[D,I],(.5[D,I]+((D-I) rotated 90))] =whatever[.5[D,H],(.5[D,H]+((D-H) rotated 90))]; % circle radius r=arclength(I--N); draw A--B--C--cycle;draw A--G;draw B--H;draw C--I; draw fullcircle scaled 2r shifted N; NinepointsLabelsAndDots; endfig; end;