2013 IMO Shortlist G1

Let $A B C$ be an acute-angled triangle with orthocenter $H$, and let $W$ be a point on side $B C$. Denote by $M$ and $N$ the feet of the altitudes from $B$ and $C$, respectively. Denote by $\omega_{1}$ the circumcircle of $B W N$, and let $X$ be the point on $\omega_{1}$ which is diametrically opposite to $W$. Analogously, denote by $\omega_{2}$ the circumcircle of $C W M$, and let $Y$ be the point on $\omega_{2}$ which is diametrically opposite to $W$. Prove that $X, Y$ and $H$ are collinear. (Thaliand)

设 $A B C$ 为锐角三角形，垂心为 $H$，$W$ 为边 $B C$ 上的一点。 $M$ 和 $N$ 分别表示从 $B$ 和 $C$ 开始的高度英尺。用$\omega_{1}$表示$B W N$的外接圆，并令$X$为$\omega_{1}$上与$W$直径相反的点。类似地，用$\omega_{2}$表示$C W M$的外接圆，并令$Y$为$\omega_{2}$上与$W$直径相反的点。证明$X、Y$和$H$共线。 (泰国)