Apollonius's problem

Hi all.

I recently was in need of a solver for tangent circles giving 3 circles.

Native GH components CircleTT and CircleTTT don't always give all solutions, some are completely un-achievable in certain situations.

I did search in the forum (here) but with no luck...

I found out Apollonius's problem and also "understood" about inverting geometries inside a circle... clever stuff!

Did somebody already made a component/script to solve all the cases of all Apollonius's problems, given three elements (point, line, circle)?

IF not, i'm already cleaning a solver, but it will still work with just 3 elements, no tree supported.

I'm thinking to convert in it a c# component, where trees can be easier handled...

What would be the best type or component?

One with a single input, that require 3-item-sized branches, and a single output, keeping branches structure?

One with 3 inputs, point, lines, circles, where it automatically combine them eachother and then solve?

It would be useful to sort output circles in some way?

Cya!