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this hAOpefully shoudn't BE weird

Source: 2023 IMO Shortlist G1

July 17, 2024
IMO Shortlistgeometry

Problem Statement

Let ABCDEABCDE be a convex pentagon such that ∠ABC=∠AED=90∘\angle ABC = \angle AED = 90^\circ. Suppose that the midpoint of CDCD is the circumcenter of triangle ABEABE. Let OO be the circumcenter of triangle ACDACD.
Prove that line AOAO passes through the midpoint of segment BEBE.
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