Area of the Arbelos

radius r

9

radius R

5

shaded area = πrR = 141.372

Archimedes (287 BC) proved that the shaded area (known as the arbelos, which means the shoemaker's knife) is equal to the area of the red circle with diameter BC. Note that BC is perpendicular to AD. The radii of the semicircles with diameters AB and BD are

r

and

R

, respectively.