have you have ruled out just deleting the circle and recreating it using the correct radius?
You can do this as follows:
Note that this tool does not maintain the original polygons centroid.
I followed domrorke's instructions and it worked most of the time. When it stopped working, I clicked 'Add Vertex' on the 'Edit Vertices' toolbar, hovered the cursor over the edge of the circular feature (not on the one visible vertex), did a left mouse click and was able to drag to resize the circle. An alternative if domrorke's instructions stop working, save your map, close and reopen ArcMap and the instructions should start working again.