The centres of a set circles, each of radius 3, lie on the circle $x^2+y^2=25.$ The locus of any point in the set is 
 

$$\begin{gathered} \mathrm{Given} \mathrm{circle} {\mathrm{x}}^2+{\mathrm{y}}^2=25 \\ Let C lie on x^2+y^2=25 \\ Let S be the set of circles with radius 3 and center (h,k) \\ Any point P(h,k) on S will be 3 units from center C. \\ Dis\tan ce from origin will be at least 5–3=2 and at most 5+3=8 \\ ⟹2\le \sqrt{h^2+k^2} \le 8 \\ \Rightarrow 4\le h^2+k^2\le 64 \\ Locus is 4\le x^2+y^2\le 64 \end{gathered}$$