Question 13
The incircle $\Omega$ of the acute-angled triangle $ABC$ is tangent to $BC$ at $K$. Let $AD$ be an altitude of triangle $ABC$ and let $M$ be the midpoint of $AD$. If $N$ is the other common point of $\Omega$ and $KM$, prove that $\Omega$ and the circumcircle of triangle $BCN$ are tangent at $N$.