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Angle inequality in acute triangle with orthocenter

Source: XVII Tuymaada Mathematical Olympiad (2010), Senior Level

July 31, 2011
inequalitiesgeometrycircumcircle

Problem Statement

In acute triangle ABCABC, let HH denote its orthocenter and let DD be a point on side BCBC. Let PP be the point so that ADPHADPH is a parallelogram. Prove that ∠DCP<∠BHP\angle DCP<\angle BHP.
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