Explanation

(b)
Since, two chords bisect each other, it means both the chords passes through the centre of circle.
$\therefore$ Length of chords are equal
$ie,\ \ \ a^{2} - 1 = 3(a + 1)$
$\Rightarrow \ \ \ a^{2} - 3a - 4 = 0$
$\Rightarrow \ \ \ \ (a - 4)(a + 1) = 0$
$\Rightarrow \ \ \ a = 4\ \ \ \ \ (\because\ \ a = - 1\ \ is\ not\ possible)$
$\therefore$ Radius of circle$= \frac{a^{2} - 1}{2} = \frac{16 - 1}{2}$
$= \frac{15}{2}$