# Name for this problem regarding chords, and the area between two closed convex curves?

I want to read more about the amazing result that, when given a closed, convex curve in the plane that can be traversed internally by a chord of length $p$+$q$, and on that chord lying at p, a point, the path of which traces another curve inside the first, the area between these curves is $\pi$$p$$q$.

I have forgotten the name of this result. Haddart? I can't seem to find it. If someone knowns what I mean, please reveal.

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Draw a smooth, closed, convex curve $C_1$. Place a chord of constant length inside curve $C_1$, and let the chords slide around the curve so that the two ends of the chord touch $C_1$ at all times. Label a point on the stick so that it divides the stick into two parts of length $p$ and $q$. As you move the stick, the point traces out a new closed curve $C_2$ within the original curve. Assuming that $C_1$ is shaped in such a way that the stick can actually pass around $C_1$ once, Holditch's theorem states the area between the curves $C_1$ and $C_2$ will be $\pi qp$. Interestingly, this area is totally independent of the shape of $C_1$.