Question 55
Let $ABC$ be an acute triangle with orthocenter $H$, and let $W$ lie strictly between $B$ and $C$ on side $BC$. Let $M,N$ be the feet of the altitudes from $B,C$, respectively. Let $\omega_1$ be the circumcircle of $BWN$, and let $X$ be the point of $\omega_1$ for which $WX$ is a diameter. Similarly, let $\omega_2$ be the circumcircle of $CWM$, and let $Y$ be the point of $\omega_2$ for which $WY$ is a diameter. Prove that $X,Y,H$ are collinear.