Circles $K_1$ and $K_2$ are externally tangent to each other at $A$ and are internally tangent to a circle $K$ at $A_1$ and $A_2$ respectively. The common tangent to $K_1$ and $K_2$ at $A$ meets $K$ at point $P$. Line $PA_1$ meets $K_1$ again at $B_1$ and $PA_2$ meets $K_2$ again at $B_2$. Show that $B_1B_2$ is a common tangent of $K_1$ and $K_2$.