Middle European Mathematical Olympiad 2022 Problem T-5

Let $\Omega$ be the circumcircle of a triangle $ABC$ with $\angle CAB = 90^{\circ}$. The medians through $B$ and $C$ meet $\Omega$ again at $D$ and $E$, respectively. The tangent to $\Omega$ at $D$ intersects the line $AC$ at $X$ and the tangent to $\Omega$ at $E$ intersects the line $AB$ at $Y$. Prove that the line $XY$ is tangent to $\Omega$.