Problem (2023G1): Let $ABCDE$ be a convex pentagon such that $\angle ABC = \angle AED = 90^\circ$. Suppose that the midpoint of $CD$ is the circumcenter of triangle $ABE$. Let $O$ be the circumcenter of triangle $ACD$. Prove that line $AO$ passes through the midpoint of segment $BE$.
AlphaGeometry formalization: a c d = triangle; m = midpoint c d; b = on_circle m a, on_dia a c; e = on_circle m a, on_dia a d; o = circumcenter a c d; n = midpoint b e ? coll a o n
HAGeo formalization: A C D = triangle; M = midpoint C D; (AC) = circle_diameter A C; (M,A) = circle_center_point M A; B = intersection (AC) (M,A); (AD) = circle_diameter A D; E = intersection (AD) (M,A); O = circumcenter A C D; N = midpoint B E; Prove: collinear A O N
Difficulty score: 2.1