ILL 1976 Problem 36

Three concentric circles with common center $O$ are cut by a common chord in successive points $A, B, C$ . Tangents drawn to the circles at the points $A, B, C$ enclose a triangular region. If the distance from point $O$ to the common chord is equal to $p$ , prove that the area of the region enclosed by the tangents is equal to $$\frac{AB \cdot BC \cdot CA}{2p}$$