¶ 2000 AMC8 Problem 19
Problem:
Three circular arcs of radius units bound the region shown. Arcs and are quarter-circles, and arc is a semicircle. What is the area, in square units, of the region?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Divide the semicircle in half and rotate each half down to fill the space below the quarter-circles. The figure formed is a rectangle with dimensions and . The area is .
Slide into and into \teIV as indicated by the arrows to create the rectangle.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions