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Angle equal

Source: Netherlands Team Selection Test 2016 Day 1-Problem 1

September 22, 2016
geometry

Problem Statement

Let △ABC\triangle ABC be a acute triangle. Let HH the foot of the C-altitude in ABAB such that AH=3BHAH=3BH, let MM and NN the midpoints of ABAB and ACAC and let PP be a point such that NP=NCNP=NC and CP=CBCP=CB and BB, PP are located on different sides of the line ACAC. Prove that ∡APM=∡PBA\measuredangle APM=\measuredangle PBA.
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