KöMaL 2015 B4704

The circles $k_2$ and $k_3$ have different radii. A circle $k_1$ touches both of them from the inside. The circles $k_2$ and $k_3$ are tangent to a circle $k_4$ from the inside. Show that the radical axis of $k_1$ and $k_4$ passes through the external point of similitude of $k_2$ és $k_3$.