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collinear circumcenters wanted, <AMC = < BAC = < ACK, AM median

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2013 Seniors p2

September 3, 2020
geometryequal anglescollinearCircumcenterChampions Tournament

Problem Statement

About the triangle ABCABC it is known that AMAM is its median, and ∠AMC=∠BAC\angle AMC = \angle BAC. On the ray AMAM lies the point KK such that ∠ACK=∠BAC\angle ACK = \angle BAC. Prove that the centers of the circumcircles of the triangles ABC,ABMABC, ABM and KCMKCM lie on the same line.
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