.geometry "version 0.40";
v1 = .free(-0.658046, -0.218279, "A");
v2 = .free(0.0128399, 0.892376, "B");
v3 = .free(0.802496, -0.0866696, "C");
l1 = .l.vv(v1, v2);
l2 = .l.vv(v2, v3);
l3 = .l.vv(v3, v1);
l4 = .l.vlperp(v2, l3);
l5 = .l.vlperp(v1, l2);
l6 = .l.vlperp(v3, l1);
v5 = .vonl(l5, -0.451593, -0.0517628, "A'");
v6 = .vonl(l4, 0.100158, -0.0766445, "B'");
v7 = .vonl(l6, 0.191829, 0.282201, "C'");
l7 = .l.vv(v5, v6, .magenta);
l8 = .l.vv(v6, v7, .magenta);
l9 = .l.vv(v7, v5, .magenta);
v9 = .v.vvmid(v5, v6, .magenta);
v10 = .v.vvmid(v6, v7, .magenta);
v11 = .v.vvmid(v7, v5, .magenta);
l10 = .l.vlperp(v11, l3, .yellow, .longline);
l11 = .l.vlperp(v10, l2, .yellow, .longline);
l12 = .l.vlperp(v9, l1, .yellow, .longline);
.text("If A', B', and C' are selected on the altitudes
of \triangleABC, and perpendiculars from the
midpoints of \triangleA'B'C' are dropped to the
sides of \triangleABC, those perpendiculars are
concurrent.  Move A, B, C, A', B', or C'.", .l0);
l16 = .l.vv(v5, v10, .red);
l17 = .l.vv(v7, v9, .red);
v4 = .v.ll(l16, l17, .red, "M");
v8 = .v.ll(l4, l5, .red, "H");
v12 = .v.ll(l10, l11, .red, "O");
l19 = .l.vv(v8, v4, .red, .display);
l20 = .l.vv(v4, v12, .red, .display);