This is a problem from my calculus 3 class.

"Find equations of two spheres that are centered at the origin and are tangent to the sphere of radius 1 centered at (3,-2,4)."

So for the sphere they give, I have figured out the equation (or at least I hope I did), which is:

(x-3)^2 + (y+2)^2 + (z-4)^2 = 1

I figure the two spheres I need to find are going to be tangent to the given sphere internally and externally, meaning they will overlap. My question however is what direction I go about now to solve the radii of the two spheres?

I'm working on the problem as we speak, maybe I just need a light bulb moment?