KöMaL 2012 C1126

$AB$ is a diameter of a circle of radius 30 cm centred at $O_1$. This circle is touched from the inside by two other circles: at point $A$ by a circle of radius 15 cm centred at $O_2$, and at point $B$ by a circle of radius 10 cm centred at $O_3$. What is the radius of the circles that touch all three of these circles?