Sorry, my bad. It’s a tricky one then.
Sounds like scripting could help, so I drafted up this Python example, but not sure how much would it be helpful:

It uses Rhino.Geometry.Circle.TryFitCircleTTT method.

tA parameter is identical to picking the first point using Circle command, Tangent option.

tB parameter is identical to picking the second point on the first curve.

tC is identical to picking the third point on the second curve, but it’s calculated in Python instead of being parameter because some values will produce invalid circles. When drawing the circle with Rhino command, the third point is actually also calculated because you’re only picking the curve, not the point, so it makes sense to calculate it in Python.