Question 78
Triangle $ABC$ ($AB\gt BC$) is inscribed in a circle $\Omega$. Points $M,N$ are chosen on $AB,BC$, respectively, so that $AM=CN$. Lines $MN,AC$ meet at $K$. Let $P$ be the incenter of triangle $AMK$, and $Q$ the excenter of triangle $CNK$ whose excircle touches side $CN$. Prove that the midpoint of arc $ABC$ of $\Omega$ is equidistant from $P,Q$.
(M. Kulgozhin)
(M. Kulgozhin)