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Circumcircle intersections everywhere

Source: Indonesian Mathematical Olympiad 2013 Problem 2

September 5, 2013
geometrycircumcirclegeometry unsolved

Problem Statement

Let ABCABC be an acute triangle and ω\omega be its circumcircle. The bisector of ∠BAC\angle BAC intersects ω\omega at [another point] MM. Let PP be a point on AMAM and inside △ABC\triangle ABC. Lines passing PP that are parallel to ABAB and ACAC intersects BCBC on E,FE, F respectively. Lines ME,MFME, MF intersects ω\omega at points K,LK, L respectively. Prove that AM,BL,CKAM, BL, CK are concurrent.
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