A well-known problem that dates back to antiquity.
Find the shaded area in terms of .
If the radii of the small circles are and respectively and the radius of the big circle we must have .
By the Intersecting Chords Theorem (Euclid Bk 2 Prop 35) we have , or .
The shaded area is
and
which equals .
Tags: arbelos, cut the knot
