Problem:
A circle of radius is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The semicircle has radius and total area . The area of the circle is . The fraction of the area that is not shaded is , and hence the fraction of the area that is shaded is also .
The problems on this page are the property of the MAA's American Mathematics Competitions