Proof of Monge's Theorem

[totonnyy]

I don't quite understand the proof of Monge's Theorem from the wiki.

"Let the three circles correspond to three spheres of the same radii; the circles correspond to the equators that result from a plane passing through the centers of the spheres. The three spheres can be sandwiched uniquely between two planes. Each pair of spheres defines a cone that is externally tangent to both spheres, and the apex of this cone corresponds to the intersection point of the two external tangents, i.e., the external homothetic center. Since one line of the cone lies in each plane, the apex of each cone must lie in both planes, and hence somewhere on the line of intersection of the two planes. Therefore, the three external homothetic centers are collinear."

Could anyone explain a little bit more?

Thanks!!

 

[Dr.Peterson]

You're quoting from https://en.wikipedia.org/wiki/Monge's_theorem . It's a very nice proof!

What parts are you having trouble with? I could try to explain each part in more detail, but it will be easier to focus on the parts you need. Are there some terms you aren't familiar with, or are you unable to visualize the various cones and planes, for example? Which parts do you understand?