Mamikon's Theorem

Theorem: All oval rings swept out by a line segment of given length that is tangent to every point of a smooth closed curve have equal areas, regardless of the size or shape of the inner curve. Moreover, the area de­pends only on the length of the tangent segment and is equal to , the area of a circular disk of radius , as if the tangent segment was rotated about a single point. Reference: Mamikon Mnatsakanian, "Annular Rings of Equal Area," Math Horizons, 5(3), 1997 pp. 5–8.