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equal angles wanted and given, right angle for point on median

Source: 2014 XVII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p8

May 7, 2021
geometryequal anglesUkrainian TYM

Problem Statement

In the triangle ABCABC on the ray BABA mark the point KK so that ∠BCA=∠KCA\angle BCA= \angle KCA , and on the median BMBM mark the point TT so that ∠CTK=90o\angle CTK=90^o . Prove that ∠MTC=∠MCB\angle MTC=\angle MCB .
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