SHARYGIN 2016 Problem 12

Let $BB_1$ be the symmedian of a nonisosceles acute-angled triangle $ABC$ . Ray $BB_1$ meets the circumcircle of $ABC$ for the second time at point $L$ . Let $AH_A, BH_B, CH_C$ be the altitudes of triangle $ABC$ . Ray $BH_B$ meets the circumcircle of $ABC$ for the second time at point $T$ . Prove that $H_A, H_C, T, L$ are concyclic.