Let C_1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C_2 be the circle with centre (1,3) that touches C_1…

Let $\displaystyle \mathrm{C}_1$ be the circle in the third quadrant of radius $\displaystyle 3$ , that touches both coordinate axes. Let $\displaystyle \mathrm{C}_2$ be the circle with centre $\displaystyle (1,3)$ that touches $\displaystyle \mathrm{C}_1$ externally at the point $\displaystyle (\alpha, \beta)$. If $\displaystyle (\beta-\alpha)^2=\frac{m}{n}$ , $\displaystyle \operatorname{gcd}(m, n)=1$, then $\displaystyle m+n$ is equal to