Question 127
Let $ABC$ be a scalene acute triangle with orthocenter $H$. The circle with center $A$ and radius $AH$ meets the circumcircle of $\triangle BHC$ at the point $T_a \neq H$. Points $T_b$ and $T_c$ are defined similarly. Prove that $H$ lies on the circumcircle of $\triangle T_a T_b T_c$.