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