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triangle construction, given 2 rays and 1 point, incircle, excircle related

Source: 2018 XXI All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p16

May 5, 2021
geometryconstructionUkrainian TYM

Problem Statement

Let K,TK, T be the points of tangency of inscribed and exscribed circles to the side BCBC triangle ABCABC, MM is the midpoint of the side BCBC. Using a compass and a ruler, construct triangle ABC given rays AKAK and ATAT (points K,TK, T are not marked on them) and point MM.
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