Question: One of the most beautiful sentences...

...the essence of plane geometry is hidden within the following puzzle:
Given is a closed curve C. It is assumed to be non-self-intersecting, convex, and continuously differentiable everywhere (a closed Jordan curve). Let line segment AB be a chord of this curve, having a fixed length l. A point P lies on this chord at a fixed distance a from A and b from B, such that l = a + b. An orientation (or direction of circulation) is now assigned to the curve. The chord is then moved continuously along the closed curve in this assigned direction of circulation. As it moves, point P traces out a so-called locus curve O, which—upon completion of one full revolution of the chord—also forms a closed curve lying entirely within C.
The task is to calculate the area of ​​the region between C and O (i.e., the area lying inside C but outside O). Divide the result by the product of a and b, and then apply the "identify" function to the outcome.