Question 108
Let $A B C D E$ be a convex pentagon circumscribed around a circle $\omega$ such that $A B \| C D$ and $B C \| D E$. Locate points $X$ and $Y$ on rays $A B$ and $E D$, respectively, such that $B X = A B$ and $D Y = D E$. Prove that $X Y$ is tangent to $\omega$.