MathNet 2019-part-01 — 184 problems (EN–VI) Question 147

Let $O$ be the circumcenter and $H$ be the orthocenter of an acute-angled triangle $ABC$. Point $T$ is the midpoint of the segment $AO$. The perpendicular bisector of $AO$ intersects the line $BC$ at point $S$.
Prove that the circumcircle of the triangle $AST$ bisects the segment $OH$.