2 circles in a greater circle, geometry problem

Question

On a diameter $AB$ of a circle, point $M$ is chosen. Around point $M$ 2 lesser circles are drawn that lie inside original circle. If $BK$ and $BK_1$ are chordes of greater circle that are tangent to two lesser circles at points $P$ and $P_1$, how can I show that $KP/PB=K_1P_1/P_1B$?

I tried looking for similarity of triangles but got nothing. Could you please give me a hint how to approach this problem?

Answer 1

Since $AKB$ and $MPB$ are both right triangles, $AK$ and $MP$ are parallels. Thus $\frac{KB}{PB}=\frac{AB}{MB}$.