I would use the path editor and a small script
Just create a "Path" with 3 points on the arc (the farthest apart for accuracy).
The write a small script in Python or Scheme that retrieves the points coordinates from the path and computes the circle center/radius (intersection of any two of the perpendicular bisectors).
This can be done with either Gimp or Inkscape. I can help with the Gimp+Python solution if needed.