TR-MO 2022 Problem 1

In triangle $ABC$ , $M$ is the midpoint of side $BC$ , the bisector of angle $BAC$ intersects $BC$ and $(ABC)$ at $K$ and $L$ , respectively. If the circle with diameter $[BC]$ is tangent to the external angle bisector of angle $BAC$ , prove that this circle is tangent to $(KLM)$ as well.