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Equal area only if orthocenter-connecting is perpendicular

Source: 2012 Indonesia Round 2 TST 1 Problem 3

February 26, 2012
geometrygeometry proposed

Problem Statement

Given a convex quadrilateral ABCDABCD, let PP and QQ be points on BCBC and CDCD respectively such that ∠BAP=∠DAQ\angle BAP = \angle DAQ. Prove that the triangles ABPABP and ADQADQ have the same area if the line connecting their orthocenters is perpendicular to ACAC.
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