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circumcenter of XYM lies on BC, excircle and circumcircles related

Source: Ukraine TST 2014 p4

May 1, 2020
geometrycircumcircleexcircleCircumcenter

Problem Statement

The AA-excircle of the triangle ABCABC touches the side BCBC at point KK. The circumcircles of triangles AKBAKB and AKCAKC intersect for the second time with the bisector of angle AA at points XX and YY respectively. Let MM be the midpoint of BCBC. Prove that the circumcenter of triangle XYMXYM lies on BCBC.
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