In right triangle \(ABC\) with right angle \(C\), \(CA = 30\) and \(CB = 16\). Its legs \(CA\) and \(CB\) are extended beyond \(A\) and \(B\). Points \(O_1\) and \(O_2\) lie in the exterior of the triangle and are the centers of two circles with equal radii. The circle with center \(O_1\) is tangent to the hypotenuse and to the extension of leg \(CA\), the circle with center \(O_2\) is tangent to the hypotenuse and to the extension of leg \(CB\), and the circles are externally tangent to each other. The length of the radius of either circle can be expressed as \(p/q\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).

(第二十五届AIME1 2007 第9题)