Circles $$\mathcal{C}_{1}$$ and $$\mathcal{C}_{2}$$ intersect at two points, one of which is $$(9,6)$$, and the product of the radii is $$68$$. The x-axis and the line $$y = mx$$, where $$m > 0$$, are tangent to both circles. It is given that $$m$$ can be written in the form $$a\sqrt {b}/c$$, where $$a$$, $$b$$, and $$c$$ are positive integers, $$b$$ is not divisible by the square of any prime, and $$a$$ and $$c$$ are relatively prime. Find $$a + b + c$$.

(第二十届AIME2 2002 第15题)