Problem

Source: Tuymaada Junior 2006 p1

Tags: geometry, right triangle, isosceles, equal segments



On the equal AC and BC of an isosceles right triangle ABC , points D and E are marked respectively, so that CD=CE. Perpendiculars on the straight line AE, passing through the points C and D, intersect the side AB at the points P and Q.Prove that BP=PQ.