MK-MO 2023 Problem 4

Let $ABC$ be a scalene acute triangle with orthocenter $H$ . The circle with center $A$ and radius $AH$ meets the circumcircle of $BHC$ at $T_{a} \neq H$ . Define $T_{b}$ and $T_{c}$ similarly. Show that $H$ lies on the circumcircle of $T_{a}T_{b}T_{c}$ .

Authored by Nikola Velov