3. The Arbelos In the Book of Lemmas (a collection of 13 geometrical propositions that has come down to us only in an Arabic translation), Archimedes introduced a figure that, owing to its shape, is known as the arbelos, or "shoemaker's knife" shown as the grey area below. Prove that if PC is the straight line perpendicular to AB at C, then the area of the shoemaker's knife equals the area of the circle whose diameter is PC. B

Fig: 1