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Has the circle theory been overturned?
Has not been overthrown

Two concentric circles, the part between them is a circle, or the circle is a figure obtained by digging a concentric circle from a big circle.

The area of a ring is pi multiplied by the sum of the radius of a big circle and the radius of a small circle and then multiplied by the difference between the radius of a big circle and the radius of a small circle. This is the area formula of the ring.