Quick Answer:

Trace the rim of the piece of a plate on a sheet of paper. Fold the tracing of the rim onto itself to form a crease in the paper. Repeat this process using a different part of the arc. The point where the two creases intersect is the center of a circle. This circle is the same size as the original plate. (You can use a compass to complete the circle.)

Complete Solution:

Trace the piece of a plate on a sheet of paper. Fold the tracing of the edge of the plate onto itself to form a crease in the paper. Repeat this process using a different part of the arc. The folds are along lines of symmetry for the circle that describes the shape of the original plate. These lines of symmetry contain diameters of the circle and meet at the center. The plate’s radius is the distance from the center to the rim. Its diameter is twice the radius.