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right angle wanted starting with a parallelogram and one circumcircle

Source: Ukrainian Geometry Olympiad 2017, IX p4 , XI p3

December 12, 2018
geometryparallelogramcircumcircleCircumcenterright angle

Problem Statement

Let ABCDABCD be a parallelogram and PP be an arbitrary point of the circumcircle of ΔABD\Delta ABD, different from the vertices. Line PAPA intersects the line CDCD at point QQ. Let OO be the center of the circumcircle ΔPCQ\Delta PCQ. Prove that ∠ADO=90o\angle ADO = 90^o.
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