HI Gull, hi folks.
A quick way to find the center of an exploded circle is to trace a diameter between facing endpoints. The midpoint of this line is the centerpoint of the circle. Use it and one of the endpoint on the exploded circle to redraw a new circle. Its geometry will overlapp the segments of the exploded circle. You will not have these in double, dont worry. Delete the diameter and then you can use the Dimension Tool to get the diameter or radius of the circle.
Just ideas.