MathNet 2018-part-06 — 181 problems (EN–VI) Question 158

Let $H$ be an orthocenter of an acute triangle $ABC$, and let $O$ be its circumcenter. The line $AO$ intersects segment $BC$ at $D$. Perpendicular to $BC$ with a foot $D$ intersects altitudes of $ABC$ through $B$ and $C$ at points $X$ and $Y$ respectively. Show that the circumcenter of $\triangle HXY$ is equally distant from points $B$ and $C$.

(Danylo Khilko)