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Simple but not easy. 2015 Spain Math Olympiad.

Source:

April 28, 2015
geometrynational olympiadgeometry unsolvedgeometry proposed

Problem Statement

Let ABCABC be a triangle. MM, and NN points on BCBC, such that BM=CNBM=CN, with MM in the interior of BNBN. Let PP and QQ be points in ANAN and AMAM respectively such that ∠PMC=∠MAB\angle PMC= \angle MAB, and ∠QNB=∠NAC\angle QNB= \angle NAC. Prove that ∠QBC=∠PCB \angle QBC= \angle PCB.
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