$P$ is a variable point on a circle with centre at $C$. CA and $C B$ are perpendiculars from $C$ to $x$ and $y$-axis respectively. If the locus of the centroid of $\triangle P A B$ is a circle with centre $(3,6)$ and radius equal to 1 , then the centre and radius of circle, whose centre is $C$, is.
(1) $\left(\frac{9}{2}, 9\right) \& 3$
(2) $\left(9, \frac{9}{2}\right) \& 2$
(3) $\left(\frac{9}{2}, \frac{9}{2}\right) \& 3$
(4) $(9,9), 3$
