If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0$$ intersect in two distinct point, then
A
$$r > 2$$
B
$$2 < r < 8$$
C
$$r < 2$$
D
$$r = 2.$$
Explanation
$$\left| {{r_1} - {r_2}} \right| < {C_1}{C_2}$$ for intersection
$$ \Rightarrow r - 3 < 5 \Rightarrow r < 8\,\,\,\,\,\,\,\,\,...\left( 1 \right)$$