USAMTS Intermediate

2018

Problem - 4270

Acute scalene triangle $\triangle{ABC}$ has circumcenter $O$ and orthocenter $H$. Points $X$ and $Y$,
distinct from $B$ and $C$, lie on the circumcircle of $\triangle{ABC}$ such that $\angle{BXH} = \angle{CYH} = 90^{\circ}$
.
Show that if lines $XY$, $AH$, and $BC$ are concurrent, then $OH$ is parallel to $BC$.