("Apollonius' problem is to construct circles that are tangent to three given circles in a plane")
Hi, everyone. I have a Math project due tomorrow and one of the questions I have to answer is "Can the Apollonius problem be generalized to spheres in 3D?"
I'm not exactly sure what the professor wants in this generalization, but I'm supposing it would be
"finding a plane that is tangent to three given spheres"
AND / OR
"finding a fifth sphere that is tangent to four given spheres"
I could not figure out how to solve any of these generalizations, and could not find their solutions in the web. Any help would be much appreciated! Thanks in advance.