KöMaL 2024 C1825

Line $e$ intersects circle $k_1$ in two distinct points $A$ and $B$. Circle $k_2$ is tangent to circle $k_1$ at point $C$ and to line $e$ at point $D$. Line $CD$ and circle $k_1$ intersect each other at point $T$ for the second time. Prove that $AT=TB$.