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Inscribed quadrilateral

Source: St Petersburg Olympiad 2018, Grade 10, P5

June 22, 2018
geometry

Problem Statement

ABCDABCD is inscribed quadrilateral. Line, that perpendicular to BDBD intersects segments ABAB and BCBC and rays DA,DCDA,DC at P,Q,R,SP,Q,R,S . PR=QSPR=QS. MM is midpoint of PQPQ. Prove that AM=CMAM=CM
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