Amy marks two points A and B that are 4 inches apart. She draws one circle that has segment AB as a diameter. She then draws a larger circle, which overlaps the first circle, such that the arc from A to B along its circumference is a quarter-circle. What is the total area covered by the two circles? Express your answer in terms of pi.

Answer 1

The radius of the first circle is half the length of segment AB, so it is 2 inches. The larger circle is centered on point B and has radius 2 inches, so their areas are $\pi(2^2)=4\pi$ square inches and $\pi(4^2)=16\pi$ square inches, respectively. The area inside the larger circle but outside the smaller circle is $16\pi - 4\pi = \boxed{12\pi}$ square inches.