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China Mathematical Olympiad 1992 problem4

Source: China Mathematical Olympiad 1992 problem4

September 30, 2013
geometrycircumcircleparallelogramgeometric transformationreflectiontrapezoidsymmetry

Problem Statement

A convex quadrilateral ABCDABCD is inscribed in a circle with center OO. The diagonals ACAC, BDBD of ABCDABCD meet at PP. Circumcircles of △ABP\triangle ABP and △CDP\triangle CDP meet at PP and QQ (O,P,QO,P,Q are pairwise distinct). Show that ∠OQP=90∘\angle OQP=90^{\circ}.
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