Question 75
Priscilla has been put in charge of preparing the scenery for her school play. She needs a crescent moon, and she has a cardboard circle of radius $r$ from which to cut it; so she puts the compass point on the edge of the circle, draws an arc of a circle of radius $r \sqrt{2}$ and cuts along the drawn line. What is the area of the crescent moon she obtains?
(A) $r^{2}$
(B) $\frac{\sqrt{2}}{2} \pi r^{2}$
(C) $\frac{1}{3} \pi r^{2}$
(D) $\left(\frac{\pi}{4}+\frac{1}{2}\right) r^{2}$
(E) $\left(\frac{\pi}{4}+1\right) r^{2}$
(A) $r^{2}$
(B) $\frac{\sqrt{2}}{2} \pi r^{2}$
(C) $\frac{1}{3} \pi r^{2}$
(D) $\left(\frac{\pi}{4}+\frac{1}{2}\right) r^{2}$
(E) $\left(\frac{\pi}{4}+1\right) r^{2}$