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Iran geometry

Source: Iranian TST 2018, first exam day 2, problem 4

April 8, 2018

Problem Statement

Let ABCABC be a triangle (∠A≠90∘\angle A\neq 90^\circ). BE,CFBE,CF are the altitudes of the triangle. The bisector of ∠A\angle A intersects EF,BCEF,BC at M,NM,N. Let PP be a point such that MP⊥EFMP\perp EF and NP⊥BCNP\perp BC. Prove that APAP passes through the midpoint of BCBC.
Proposed by Iman Maghsoudi, Hooman Fattahi
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