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Of midpoints and circumcenters

Source: Baltic Way 2018, Problem 13

November 6, 2018
geometrycircumcircle

Problem Statement

The bisector of the angle AA of a triangle ABCABC intersects BCBC in a point DD and intersects the circumcircle of the triangle ABCABC in a point EE. Let K,L,MK,L,M and NN be the midpoints of the segments AB,BD,CDAB,BD,CD and ACAC, respectively. Let PP be the circumcenter of the triangle EKLEKL, and QQ be the circumcenter of the triangle EMNEMN. Prove that ∠PEQ=∠BAC\angle PEQ=\angle BAC.
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