Difference between distance to a sphere and to its center

Question

I have a set of 3D points and a sphere. All the points lay outside the sphere. I want to find the point that is most close to the sphere.

The distance between a point (P) and a sphere (S) is defined as follow:

Distance(P,S) = Min [EuclideanDistance(P, Sp)] : Sp in S 

Is it enough to find the point P that is most close to the center of the sphere? Are those two operations equals?

Once again, no point lays inside the sphere.

Answer 1

Yes, you are right. If your points are outside the sphere, then the point closest to the sphere is the one which is closest to the center of the sphere.