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Concentric circles in centroid configuration

Source: Sharygin Finals 2017, Problem 8.3

August 4, 2017
geometryCentroidconcentricgeometric transformationreflection

Problem Statement

Let AD,BEAD, BE and CFCF be the medians of triangle ABCABC. The points XX and YY are the reflections of FF about ADAD and BEBE, respectively. Prove that the circumcircles of triangles BEXBEX and ADYADY are concentric.
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