Question 84
Let $\Omega$ be the circumcircle of a triangle $A B C$ with $\angle C A B = 90^\circ$. The medians through $B$ and $C$ meet $\Omega$ again at $D$ and $E$, respectively. The tangent to $\Omega$ at $D$ intersects the line $A C$ at $X$ and the tangent to $\Omega$ at $E$ intersects the line $A B$ at $Y$. Prove that the line $X Y$ is tangent to $\Omega$.