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TurkeyTST 2008 Q1

Source:

April 2, 2008
geometrygeometry unsolved

Problem Statement

In an ABC ABC triangle such that m(∠B)>m(∠C) m(\angle B)>m(\angle C), the internal and external bisectors of vertice A A intersects BC BC respectively at points D D and E E. P P is a variable point on EA EA such that A A is on [EP] [EP]. DP DP intersects AC AC at M M and ME ME intersects AD AD at Q Q. Prove that all PQ PQ lines have a common point as P P varies.
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