Problem

Source: Indonesian National Mathematical Olympiad 2024, Problem 3

Tags: geometry, circumcircle, Indonesia, orthocenter, Indonesia MO, Inamo



The triangle $ABC$ has $O$ as its circumcenter, and $H$ as its orthocenter. The line $AH$ and $BH$ intersect the circumcircle of $ABC$ for the second time at points $D$ and $E$, respectively. Let $A'$ and $B'$ be the circumcenters of triangle $AHE$ and $BHD$ respectively. If $A', B', O, H$ are not collinear, prove that $OH$ intersects the midpoint of segment $A'B'$.