TR-MO 2022 Problem 5

In triangle $ABC$ , $90^{o}> \angle A> \angle B> \angle C$ . Let the circumcenter and orthocenter of the triangle be $O$ and $H$ . $OH$ intersects $BC$ at $T$ and the circumcenter of $(AHO)$ is $X$ . Prove that the reflection of $H$ over $XT$ lies on the circumcircle of triangle $ABC$ .