Question 28
Let $ABC$ be an acute triangle with orthocenter $H$, and let $W$ lie in the interior of 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 diametrically opposite $W$ on $\omega_1$. Similarly, let $\omega_2$ be the circumcircle of $CWM$, and let $Y$ be the point diametrically opposite $W$ on $\omega_2$. Prove that $X,Y,H$ are collinear.