Let Ω1 be a circle with centre O and let AB be a diameter of Ω1 . Let P be a point on the segment OB different from O. Suppose another circle Ω2 with centre P lies in the interior of Ω1 . Tangents are drawn from A and B to the circle Ω2 intersecting Ω1 again at A1 and B1 respectively such that A1 and B1 are on the opposite sides of AB. Given that A1B = 5, AB1 = 15 and OP = 10, find the radius of Ω1.
