Problem:
The shaded region below is called a shark's fin falcata, a figure studied by Leonardo da Vinci. It is bounded by the portion of the circle of radius and center that lies in the first quadrant, the portion of the circle of radius and center that lies in the first quadrant, and the line segment from to . What is the area of the shark's fin falcata?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The shaded area is obtained by subtracting the area of the semicircle from the area of the quarter circle:
The problems on this page are the property of the MAA's American Mathematics Competitions