Question 80
Let $ABC$ be an acute triangle, $H$ its orthocentre, and $M$ the midpoint of $BC$. Furthermore, let $k_1$ and $k_2$ be the circle with diameter $AH$ and the circle with center $M$ that touches the circumcircle of triangle $ABC$ interiorly, respectively. Prove that $k_1$ and $k_2$ are touching circles.