P.o.t.W. #6 Solution
(a) The overlapping region consists of two equal segments. Find the area of one of the segments and double it. Let \({\textrm{\theta }} be the central angle between two radii drawn to the two points where the circles intersect. The area of the sector is \(\frac{1}{2}{\textrm{\theta }}\,{r^2} = \frac{1}{2}{\textrm{\theta }} . But the function, \(A\left( b \right) , must be in terms of b; so, \({\textrm{\theta }} must...