.geometry "version 0.40";
v1 = .free(-0.160484, 0.242587, "A");
v2 = .free(-0.125869, 0.727184, "C");
v3 = .free(0.481451, 0.145038, "B");
l1 = .l.vv(v1, v2);
l2 = .l.vv(v2, v3);
l3 = .l.vv(v3, v1);
v4 = .v.lvmirror(l2, v1, "A'");
v5 = .v.lvmirror(l3, v2, "C'");
v6 = .v.lvmirror(l1, v3, "B'");
l4 = .l.vv(v2, v4);
l5 = .l.vv(v4, v3);
l6 = .l.vv(v3, v5);
l7 = .l.vv(v5, v1);
l8 = .l.vv(v1, v6);
l9 = .l.vv(v6, v2);
c1 = .c.lll(l9, l1, l8, 1, .cyan);
c2 = .c.lll(l4, l5, l2, 1, .cyan);
c3 = .c.lll(l3, l6, l7, 1, .cyan);
v7 = .v.ccenter(c1, .cyan);
v8 = .v.ccenter(c2, .cyan);
v9 = .v.ccenter(c3, .cyan);
l13 = .l.vv(v2, v9, .cyan);
l14 = .l.vv(v3, v7, .cyan);
l15 = .l.vv(v1, v8, .cyan);
.text("In \triangleABC, reflect A across BC to make A', B across AC
to make B', and C across AB to make C'. Show that
when the incenters of triangles \triangleA'BC, \triangleC'AB and \triangleB'CA
are connected to A, B, and C, respectively, those
lines are concurrent.", .l0);