Question 132
Let $BE$ and $CF$ be altitudes of an acute-angled triangle $ABC$. The segment $AD$ is the diameter of the circumcircle of $ABC$. Let $M$ be the midpoint of side $BC$. The internal common tangents of the incircles of triangles $BMF$ and $CME$ intersect at point $K$. Prove that $K$, $M$, and $D$ are collinear.