Question 156
In a triangle $ABC$ with $90^\circ \gt \hat{A} \gt \hat{B} \gt \hat{C}$ let $H$ be the orthocenter and $O$ be the circumcenter. The lines $HO$ and $BC$ intersect at point $T$. Let $X$ be the circumcenter of the triangle $AHO$. Prove that the reflection of $H$ over the line $TX$ lies on the circumcircle of $ABC$.