Let a chord of constant length be slid around a smooth, closed, convex curve , and choose a point on the chord which divides it into segments of lengths and . This point will trace out a new closed curve , as illustrated above. Provided certain conditions are met, the area between and is given by , as first shown by Holditch in 1858.
The Holditch curve for a circle of radius is another circle which, from the theorem, has radius