The figure shows a triangle ABC with the
circumcircle O. D is any point and E is a point on the circumcircle O.
Lines AD, BD, and CD meet the circumcircle O at A', B', and C',
respectively. Lines EA', EB', and EC' meet lines BC, AC, and AB at A",
B", and C", respectively. Prove that points A", B", C", and D are