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Close - they're called concentric circles.
Circles have diameters, rectangles have diagonals.
Twice max.
You can do an experiment on several circles of different diameters.
You need only know the radius of each circle to determine that they are congruent. If the radii are identical, the circles are identical. This can also be determined by comparing the diameters (twice the radii), or the circumferences, or the areas of the circles. In all cases, if the parameters are identical, the circles are identical.