In right triangle A B C with right angle C, C A=30 and C B=16. Its legs \overline{C A} and \overline{C B} 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 C A, the circle with center \mathrm{O}_{2} is tangent to the hypotenuse and to the extension of leg C B, 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.