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right angle wanted, cyclic given

Source: Russian Regional Olympiad 2010 11.3

August 24, 2024
geometryperpendicular bisectorcyclic quadrilateral

Problem Statement

Quadrangle ABCDABCD is inscribed in a circle with diameter ACAC. Points KK and MM are projections of vertices AA and CC, respectively, onto line BDBD. A line parallel to BCBC is drawn through point KK and intersecting ACAC at point PP. Prove that angle KPMKPM is a right angle.
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