3rd Asian Pacific Mathematics Olympiad 1991 Problems

3rd Asian Pacific Mathematics Olympiad 1991 ProblemsA1.  ABC is a triangle. G is the centroid. The line parallel to BC through G meets AB at B' and AC at C'. Let A'' be the midpoint of BC, C'' the intersection of B'C and BG, and B'' the intersection of C'B and CG. Prove that A''B''C'' is similar to ABC.