The Shoemaker's Knife
- Nikky Vanderhout
The area enclosed by the semi-circles centred O, X and Y and on the same diameter is called the Shoemaker's Knife. The radii of the two smaller semi-circles are variable. This is illustrated in the diagram below.
Prove that the area of the circle which has the radical axis as diameter is equal to the area of the Shoemaker's Knife.