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Parallelogram and equality of angles

Source: Serbian National Olympiad 2012, Problem 1

April 4, 2012
geometryparallelogramcircumcircletrigonometrygeometry proposed

Problem Statement

Let ABCDABCD be a parallelogram and PP be a point on diagonal BDBD such that ∠PCB=∠ACD\angle PCB=\angle ACD. Circumcircle of triangle ABDABD intersects line ACAC at points AA and EE. Prove that ∠AED=∠PEB.\angle AED=\angle PEB.
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