Problem:
A circle of radius 2 is centered at . An equilateral triangle with side 4 has a vertex at . What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let equal the area of the circle, the area of the triangle, and the area of the overlapped sector. The answer is . The area of the circle is and the area of the triangle is , so the result is .
The problems on this page are the property of the MAA's American Mathematics Competitions