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circumencter lies on perp. bisector, equilateral and 3 circumcircles related

Source: Czech-Polish-Slovak Junior Match 2018, Team p4 CPSJ

March 7, 2020
geometrycircumcirclecolinearCircumcenter

Problem Statement

A line passing through the center MM of the equilateral triangle ABCABC intersects sides BCBC and CACA, respectively, in points DD and EE. Circumcircles of triangle AEMAEM and BDMBDM intersects, besides point MM, also at point PP. Prove that the center of circumcircle of triangle DEPDEP lies on the perpendicular bisector of the segment ABAB.
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