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Interesting geometry

Source: St Petersburg Olympiad 2012, Grade 10, P6

September 29, 2017
geometryparallelogram

Problem Statement

ABCDABCD is parallelogram. Line ll is perpendicular to BCBC at BB. Two circles passes through D,CD,C, such that ll is tangent in points PP and QQ. MM - midpoint ABAB. Prove that ∠DMP=∠DMQ\angle DMP=\angle DMQ
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