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)