Explanation

(c)
The equations of the given circles are
$x^{2} + y^{2} - 10x + 16 = 0$
$\Rightarrow (x - 5)^{2} + y^{2} = 3^{2}$ …(i)
Whose centre is (5, 0) and radius=3
And $x^{2} + y^{2} = r^{2}$ …(ii)
[image:11_image87.emf]
Whose centre is (0, 0) and radius $= r$
Clearly, these two circles will intersect each other at two distinct points, if $r > OA$
$\Rightarrow r > 5 - 3\ \Rightarrow r > 2$ and $r < OB$
$\Rightarrow r < 2 + 3 + 3\ \Rightarrow r < B$
$\therefore\ 2 < r < 8$