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I need some pure geometry :))

Source: IMO Shortlist 1996 problem G3

October 4, 2003
geometrycircumcirclesymmetrytrigonometryorthocenterIMO Shortlist

Problem Statement

Let OO be the circumcenter and HH the orthocenter of an acute-angled triangle ABCABC such that BC>CABC>CA. Let FF be the foot of the altitude CHCH of triangle ABCABC. The perpendicular to the line OFOF at the point FF intersects the line ACAC at PP. Prove that ∡FHP=∡BAC\measuredangle FHP=\measuredangle BAC.
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