.geometry "version 0.51";
v1 = .free(-0.043772, 0.491317, "A");
v2 = .free(0.489162, 0.134731, "B");
v3 = .free(-0.40006, 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);
c1 = .c.lll(l7, l8, l1, 1);
c2 = .c.lll(l2, l8, l9, 1);
c3 = .c.lll(l7, l3, l9, 1);
v7 = .v.ccenter(c3, "B''");
v8 = .v.ccenter(c1, "C''");
v9 = .v.ccenter(c2, "A''");
l10 = .l.vv(v1, v9);
l12 = .l.vv(v3, v8);
l13 = .l.vv(v7, v2);
.text("The superior triangle of \triangleABC is made
with lines through its vertices parallel to the
opposite sides.  If the incenters of the newly-formed
triangles are connected to the opposite vertices, they
seem to meet at a point.  Do they?", .red);