Tangent arcs with a "convex" curve - strange behavior

… 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:
Screenshot 2024-09-26 at 20.49.28
just plug the arc into a circle parameter.

kind regards -tom

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