I think you are using the best approach, if I understand you correctly. As the site that Joy referenced explained, you draw two chords across any portions of the edge of the plate, then draw perpendicular bisectors of those chords. The point at which those two bisectors intersect is the center of the circular plate. Then measure the distance to the edge to get the radius.
You can do all this mathematically with equations. The process would be:
1. Select points A, B, and C. My advice would be to establish a coordinate system that makes these points "easy" to deal with, but it doesn't really matter.
2. Determine the slope for Chord 1 (connecting points A and B) and Chord 2 (connecting points B and C).
3. Find the midpoint of both chords. The xcoordinates of the midpoint of Chord 1 is the midpoint between the xcoordinates of points A and B and the ycoordinate of the midpoint of Chord 1 is the midpoint between the ycoordinates of points A and B. Use the same process to find the midpoint coordinate of Chord 2.
4. Determine thee equations of the bisectors of Chord 1 and the bisector of Chord 2. The bisector runs through the midpoints that you just determined, and the slope of each bisector is the negative reciprocal of the chord it bisects (that's' why we needed to find the slope if the chords in step 2). Using the form y = mx+b you have values for x, y, and m, so you can solve for b.
5. Determine the point at which the two bisectors intersect.
6. Calculate the distance from that point to either A, B, or C using the Pythagorean theorem. It doesn't matter which point A, B or C you pick  all three should yield the same distance from the center. But to check your work I suggest doing this calculation with at least two of these point, if not all three.
