Problem:
is a rectangle, is the center of the circle, and is on the circle. If and , then the area of the shaded region is between
Answer Choices:
A. and
B. and
C. and
D. and
E. and
Solution:
By the Pythagorean Theorem, . Since , the radius of the circle is . The area of the shaded region, then, is (a quarter circle with a rectangle deleted) . This quantity is clearly greater than and less than since .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions