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Classical triangle geometry

Source: Kazakhstan international contest 2006, Problem 2

January 22, 2006
geometryparallelogramanalytic geometryfunctiontrigonometrytrapezoidratio

Problem Statement

Let ABC ABC be a triangle and K K and L L be two points on (AB) (AB), (AC) (AC) such that BK \equal{} CL and let P \equal{} CK\cap BL. Let the parallel through P P to the interior angle bisector of ∠BAC \angle BAC intersect AC AC in M M. Prove that CM \equal{} AB.
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