P.S. I added a ‘Random Subset’ feature (pink group) to use a subset of the list of circles as a quick way of trying any two circles, to match your diagram. Then I found I needed to sort the circle segments differently (teal group).
This model implements two different methods, BiArc (piped) and BzSpan (white curves).
TangentCrvs_2022Feb9aa.gh (38.4 KB)