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Line passes through orthocenter 2

Source: Own- Arab Saudi TST 2016

July 29, 2016
geometry

Problem Statement

Let ABCABC be a triangle inscribed in (O)(O). Two tangents of (O)(O) at B,CB,C meets at PP. The bisector of angle BACBAC intersects (P,PB)(P,PB) at point EE lying inside triangle ABCABC. Let M,NM,N be the midpoints of arcs BCBC and BACBAC. Circle with diameter BCBC intersects line segment ENEN at FF. Prove that the orthocenter of triangle EFMEFM lies on BCBC.
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