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fixed point, related to circumcircles and orthocenter

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p5

September 8, 2019
geometrycircumcircleorthocenterfixedFixed point

Problem Statement

Given a circle and a chord ABAB, different from the diameter. Point CC moves along the large arc ABAB. The circle passing through passing through points A,CA, C and point HH of intersection of altitudes of of the triangle ABCABC, re-intersects the line BCBC at point PP. Prove that line PHPH passes through a fixed point independent of the position of point CC.