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Easy Geometry , concyclicity wanted

Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 7

March 16, 2020
geometry

Problem Statement

In △ABC\triangle ABC with AB≠ACAB\neq{AC} let MM be the midpoint of ABAB, let KK be the midpoint of the arc BACBAC in the circumcircle of △ABC\triangle ABC, and let the perpendicular bisector of ACAC meet the bisector of ∠BAC\angle BAC at PP . Prove that A,M,K,PA, M, K, P are concyclic.
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