I need help with the following problem.
Given three circles $k, k_1, k_2$. $k_1$ and $k_2$ touch internally $k$ at points $M$ and $N$ respectively. $a$ is the common interior tangent to $k_1$and $k_2$ at points $R$ and $S$. $MR \cap k = A$ and $NS \cap k = B$. Prove that $a \perp AB$.