Let _1 be a circle with centre O and let AB be diameter of _1 . Let...

Let $\Omega_1$ be a circle with centre O and let AB be diameter of $\Omega_1$. Let P be a point on the segment OB different from O . Suppose another circle $\Omega_2$ with centre P lies in the interior of $\Omega_1$. Tangents are drawn from A and B to the circle $\Omega_2$ intersecting $\Omega_1$ again at $\mathrm{A}_1$ and $\mathrm{B}_1$ respectively such that $\mathrm{A}_1$ and $B_1$ are on the opposite sides of $A B$. Given that $A_1 B=5, A B_1=15$ and $O P=10$, find the radius of $\Omega_1$.