Explanation

(d)
The radical axis of circle Ist and IInd is
$S_{1} - S_{2} = 0$
$\Rightarrow \ \ \ \left( x^{2} + y^{2} - 16x + 60 \right) - \left( x^{2} + y^{2} - 12x + 27 \right) = 0$
$\Rightarrow \ \ - 4x + 33 = 0\ \ \ \Rightarrow \ \ \ x = \frac{33}{4}$ …(i)
The radical axis of circle IInd and IIIrd is
$S_{2} - S_{3} = 0$
$\Rightarrow \ \ \ \left( x^{2} + y^{2} - 12x + 27 \right) - \left( x^{2} + y^{2} - 12y + 8 \right) = 0$
$\Rightarrow \ \ - 12x + 12y + 19 = 0$ …(ii)
$\therefore$ From Eqs. (i) and (ii), we get radical centre $\left( \frac{33}{4},\frac{20}{3} \right)$