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Four points on a circle

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September 6, 2011
geometryparallelogramgeometric transformationreflectiongeometry unsolved

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. The lines BCBC and ADAD meet at a point PP. Let QQ be the point on the line BPBP, different from BB, such that PQ=BPPQ=BP. Consider the parallelograms CAQRCAQR and DBCSDBCS. Prove that the points C,Q,R,SC,Q,R,S lie on a circle.
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