ISL 2023 G1

Let $A B C D E$ be a convex pentagon such that $\angle A B C=\angle A E D=90^{\circ}$. Suppose that the midpoint of $C D$ is the circumcentre of triangle $A B E$. Let $O$ be the circumcentre of triangle $A C D$. Prove that line $A O$ passes through the midpoint of segment $B E$. (Slovakia)