Two circles $k_1,k_2$ touch each other at $P$, and touch a line $\ell$ at $A$ and $B$ respectively. Line $AP$ meets $k_2$ at $C$. Prove that $BC$ is perpendicular to $\ell$.
Problem
Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p2a
Tags: tangent circles, geometry, circles, perpendicular