2023 IMO Shortlist 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)

令 $A B C D E$ 为凸五边形，使得 $\angle A B C=\angle A E D=90^{\circ}$。假设$C D$ 的中点是三角形$A B E$ 的外心。令 $O$ 为三角形 $A C D$ 的外心。证明线$A O$ 通过线段$B E$ 的中点。 (斯洛伐克)