Problem

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

Tags: geometry, construction, Ukrainian TYM



Let $K, T$ be the points of tangency of inscribed and exscribed circles to the side $BC$ triangle $ABC$, $M$ is the midpoint of the side $BC$. Using a compass and a ruler, construct triangle ABC given rays $AK$ and $AT$ (points $K, T$ are not marked on them) and point $M$.