TUYMAADA 2024 J4

A triangle $ABC$ is given. $N$ and $M$ are the midpoints of $AB$ and $BC$ , respectively. The bisector of angle $B$ meets the segment $MN$ at $E$ . $H$ is the base of the altitude drawn from $B$ in the triangle $ABC$ . The point $T$ on the circumcircle of $ABC$ is such that the circumcircles of $TMN$ and $ABC$ are tangent. Prove that points $T, H, E, B$ are concyclic. Proposed by M. Yumatov