Problem

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

Tags: geometry, equal angles, Ukrainian TYM



In the triangle $ABC$ on the ray $BA$ mark the point $K$ so that $\angle BCA= \angle KCA$ , and on the median $BM$ mark the point $T$ so that $\angle CTK=90^o$ . Prove that $\angle MTC=\angle MCB$ .