" January 2008 (UTC)

So glad that you liked it! )  Thanks for explaining the missing solutions, although I now realize that the trick of expanding or shrinking the radii to get a tangency doesn't always work.  How do you shrink/expand a line to keep it in contact with the separating circles?  As an aside, I've heard of Sophus Lie, but I know basically nothing about him or his sphere. P

On a whim, I worked a little more on Apollonius' problem today.  I hope you like it, too.  If you could help me understand the Gergonne solution described at MathWorld or on the Spanish interwiki, that'd be great; but if you don't have time, that's OK, too.  I'm sure that some angel will whisper the answer in my ear if I just stare at it long enough. )  Either that, or she'll whisper, ""Willow, you should clean your kitties' litterbox tonight."" ;)   20:19, 30"