English: Animation of Holditch's theorem for a smooth convex Jordan curve. The chord is split by a point into two parts of fixed lengths ${\displaystyle a}$ and ${\displaystyle b}$. As the chord slides along the black curve, the point draws the blue curve, called the locus of this point. The area of the blue region between the two curves is ${\displaystyle \pi ab}$, regardless of the size or shape of the initial curve.