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Some geometry

Source: Moscow Olympiad 2018, Grade 10, P3

July 13, 2018
geometrycircumcircle

Problem Statement

OO is circumcircle and AHAH is the altitude of △ABC\triangle ABC. PP is the point on line OCOC such that AP⊥OCAP \perp OC. Prove, that midpoint of ABAB lies on the line HPHP.
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