Explanation

(a)
The centres and radii of two circles are $C_{1}(1,\ 3),\ C_{2}(4,\ - 1)$
and $r_{1} = r,\ \ \ r_{2} = \sqrt{16 + 1 - 8} = 3$
two circles intersect in two distinct points, then
$r_{1} - r_{2} < C_{1}C_{2} < r_{1} + r_{2}$
$\Rightarrow \ \ r - 3 < \sqrt{(4 - 1)^{2} + ( - 1 - 3)^{2}} < r + 3$
$\Rightarrow \ \ r - 3 < 5 < r + 3$
$\Rightarrow \ \ \ r < 8$ and $2 < r$
$\Rightarrow \ \ 2 < r < 8$