MathDB

2

Part of 2009 Balkan MO

Problems(1)

Nice Symmedian property

Source: BMO 2009 Problem 2

4/30/2009
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
geometryBalkan Mathematics Olympiad