Question 117
Let $ABC$ be an acute angled triangle with orthocenter $H$ and circumcenter $O$. Assume the circumcenter $X$ of $BHC$ lies on the circumcircle of $ABC$. Reflect $O$ across $X$ to obtain $O'$, and let the lines $XH$ and $O'A$ meet at $K$. Let $L$, $M$ and $N$ be the midpoints of $[XB]$, $[XC]$ and $[BC]$, respectively. Prove that the points $K$, $L$, $M$ and $N$ are cocyclic.
