the minimum and the maximum distance of point $P$, outside the circle, to the circle is PB and PA respectively, where AB must be the diameter as the maximum distance between two points on a circle is the diameter only.

We have $\(\mathrm{PB}=5 \& \mathrm{PA}=11\)$, so we get $\(\mathrm{AB}=\mathrm{PA}-\mathrm{PB}=11-5=6\)$ which is equal to 2 r , where r is the radius of the circle. So, we get $\(\mathrm{r}=3\)$.

Finally the distance of point P from the centre of the circle C is $\(\mathrm{PB}+\mathrm{BO}=5+3=8\)$
Hence the answer is (E).