Problem

Source: Iranian National Olympiad (3rd Round) 2007

Tags: geometry, geometric transformation, reflection, parallelogram, geometry proposed



Let ABC, l and P be arbitrary triangle, line and point. A,B,C are reflections of A,B,C in point P. A is a point on B'C' such that AA''\parallel l. B'',C'' are defined similarly. Prove that A'',B'',C'' are collinear.