Question 181
Given an acute triangle $ABC$ with its altitudes $AD$, $BE$, $CF$ concurrent at $H$. The point $K$ changes on the segment $AH$. Let $M$, $N$ be the projections of $H$ on the lines $KE$, $KF$. Prove that the line joining the circumcenters of triangles $HEN$ and $HFM$ always passes through a fixed point.