Hi Brian,

re:
> I think that the CircleTan command has the Apollonius algebra built in.

CircleTan uses an iterative solver technique - that's when given some "seed points" to start with it takes little steps on each curve and sees which directions are getting closer to a good result. Then smaller and smaller steps to converge in on the answer.

The tricky part with that kind of solver is getting good seed points, it tends to work well when you can guide it by picks in the general region where you think the answer should be.

The good part about it is that it's very general purpose, it can find a circle tangent to 3 general curves, not just 3 circles:


- Michael