KöMaL 2023 B5339

A circle $k_1$ touches another circle $k_2$ from the inside at point $P$. Let $M$ denote an arbitrary point on the circumference of $k_1$, and let the tangent drawn to $k_1$ at $M$ intersect $k_2$ at points $A$ and $B$. Show that $PM$ bisects the angle $APB$.