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locus wanted, altitudes and circumcircle realted

Source: 2013 XVI All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p6

May 11, 2021
geometryLocusUkrainian TYM

Problem Statement

Given a circle ω\omega, on which marks the points A,B,CA,B,C. Let BFBF and CECE be the altitudes of the triangle ABCABC, MM be the midpoint of the side ACAC. Find a the locus of the intersection points of the lines BFBF and EMM for all positions of point AA , as AA moves on ω\omega.
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