.geometry "version 0.51";
v1 = .free(-0.0598802, 0.598802, "A");
v2 = .free(0.458084, 0.0808383, "B");
v3 = .free(-0.47006, 0.0272455, "C");
l1 = .l.vv(v1, v2);
l2 = .l.vv(v2, v3);
l3 = .l.vv(v3, v1);
l4 = .l.vlpar(v1, l2, .in);
l5 = .l.vlpar(v3, l1, .in);
l6 = .l.vlpar(v2, l3, .in);
v4 = .v.ll(l6, l4);
v5 = .v.ll(l4, l5);
v6 = .v.ll(l5, l6);
l7 = .l.vv(v5, v4);
l8 = .l.vv(v4, v6);
l9 = .l.vv(v6, v5);
.text("The superior triangle of \triangleABC is formed
by constructing lines parallel to its sides passing
through the opposide vertices.  Connect the nine-point
centers of the newly-formed triangles to those opposite
vertices and they seem to meet at a point.  Do they?", .red);
v7 = .v.vvmid(v1, v4);
v8 = .v.vvmid(v4, v2);
v9 = .v.vvmid(v2, v1);
v10 = .v.vvmid(v1, v3);
v11 = .v.vvmid(v3, v5);
v12 = .v.vvmid(v5, v1);
v13 = .v.vvmid(v3, v2);
v14 = .v.vvmid(v2, v6);
v15 = .v.vvmid(v6, v3);
c1 = .c.vvv(v9, v7, v8);
c2 = .c.vvv(v13, v14, v15);
c3 = .c.vvv(v10, v12, v11);
v16 = .v.ccenter(c1, "C'");
v17 = .v.ccenter(c3, "B'");
v18 = .v.ccenter(c2, "A'");
l10 = .l.vv(v1, v18);
l13 = .l.vv(v3, v16);
l14 = .l.vv(v2, v17);