Arbelos properties v1

Two semi-circles within a bigger circle make this geometrical shape, Arbelos, which has very interesting properties. The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient cobblers (Gardner 1979). Archimedes himself is believed to have been the first mathematician to study the mathematical properties of this figure. The position of the central notch is arbitrary and can be located anywhere along the diameter. (Credit: WolframMathWorld)