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Nice Symmedian property

Source: BMO 2009 Problem 2

April 30, 2009
geometryBalkan Mathematics Olympiad

Problem Statement

Let MN MN be a line parallel to the side BC BC of a triangle ABC ABC, with M M on the side AB AB and N N on the side AC AC. The lines BN BN and CM CM meet at point P P. The circumcircles of triangles BMP BMP and CNP CNP meet at two distinct points P P and Q Q. Prove that ∠BAQ=∠CAP \angle BAQ = \angle CAP.
Liubomir Chiriac, Moldova
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