MathDB
Points on a triangle

Source: ToT Junior O Level Autumn 1998

October 5, 2008
geometry proposedgeometry

Problem Statement

In a triangle ABC ABC the points A A', B B' and C C' lie on the sides BC BC, CA CA and AB AB, respectively. It is known that \angle AC'B' \equal{} \angle B'A'C, \angle CB'A' \equal{} \angle A'C'B and \angle BA'C' \equal{} \angle C'B'A. Prove that A A', B B' and C C' are the midpoints of the corresponding sides.