BALTIC-WAY 2022 Problem 15

Let $\Omega$ be a circle, and $B, C$ are two fixed points on $\Omega$ . Given a third point $A$ on $\Omega$ , let $X$ and $Y$ denote the feet of the altitudes from $B$ and $C$ , respectively, in the triangle $ABC$ . Prove that there exists a fixed circle $\Gamma$ such that $XY$ is tangent to $\Gamma$ regardless of the choice of the point $A$ .