January  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 doesnt always work  How do you shrinkexpand a line to keep it in contact with the separating circles  As an aside Ive 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 thatd be great but if you dont have time thats OK too  Im sure that some angel will whisper the answer in my ear if I just stare at it long enough   Either that or shell whisper Willow you should clean your kitties litterbox tonight