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Angles in parallelogram

Source: Mexican Mathematical Olympiad 2013 Problem 2

December 1, 2013
geometryparallelogramgeometry proposed

Problem Statement

Let ABCDABCD be a parallelogram with the angle at AA obtuse. Let PP be a point on segment BDBD. The circle with center PP passing through AA cuts line ADAD at AA and YY and cuts line ABAB at AA and XX. Line APAP intersects BCBC at QQ and CDCD at RR. Prove ∠XPY=∠XQY+∠XRY\angle XPY = \angle XQY + \angle XRY.
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