Holditch's_theorem
Holditch's theorem
On the area enclosed by a point on a rigid chord rotating inside a convex closed curve
In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance p from one end and a distance q from the other is a closed curve whose enclosed area is less than that of the original curve by . The theorem was published in 1858 by Rev. Hamnet Holditch.[1][2] While not mentioned by Holditch, the proof of the theorem requires an assumption that the chord be short enough that the traced locus is a simple closed curve.[3]