… i also just saw this thread.
looks like a nice geometric challenge…
and it is a unsatisfying rainy day today… so hopefully this helps:
construction
Circle A B and given Radius R = 200
draw additional concentric circles with
R+rA
R-rA
around Center of A … same for B
the intersections of the “+r” and “-r” circles are already the searched center points.
some additional lines from the new Centers to the old Centers will give the start/endpoints of the searched arcs.
… a similar construction is found here as video
CircleTangentTangentR.3dm (2.9 MB)
grasshopper script
implementing above as c# script.
The script does not care about special cases (180-degree-arcs)
I tried to keep everything sorted. The order of input Circles matters.
Did only test in 2d / WorldXY
CircleTangentTangentR_tomp_02.gh (16.1 KB)
arc vs circle
please note that a cicle can be easily extracted from an arc:
just plug the arc into a circle parameter.
kind regards -tom