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

 
Let (h, k) be any point in the set. Then the equation of circle is  ${(x-h)}^2+{(y-k)}^2=9$
But (h, k) lies on  $x^2+y^2=25$. Therefore,
$h^2+k^2=25$
$\therefore 2\le$ distance between the centers of two circles $\le 8\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}or\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}4\le h^2+k^2\le 64$    
Therefore, the locus of (h, k) is $4\le x^2+y^2\le 64$ .