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orthocenter, perpendicular chords, AP = 2PB (Kyiv City Olympiad 2009 8.5 9.3)

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July 2, 2020
geometryChordsorthocentercircle

Problem Statement

A chord ABAB is drawn in the circle, on which the point PP is selected in such a way that AP=2PBAP = 2PB. The chord DEDE is perpendicular to the chord ABAB and passes through the point PP. Prove that the midpoint of the segment APAP is the orthocener of the triangle AEDAED.
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