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Parallelogram geometry

Source: St Petersburg Olympiad 2015, Grade 11, P4

October 17, 2017
geometrycircumcircleparallelogram

Problem Statement

ABCDABCD is convex quadrilateral. Circumcircle of ABCABC intersect ADAD and DCDC at points PP and QQ. Circumcircle of ADCADC intersect ABAB and BCBC at points SS and RR. Prove that if PQRSPQRS is parallelogram then ABCDABCD is parallelogram
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