Problem:
The figure below shows a large unshaded circle with a number of smaller unshaded and shaded circles in its interior. What fraction of the interior of the large unshaded circle is shaded?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
WLOG, assume that each square has a side length of units. This means that there are shaded unit circles, which total to area. There is also a shaded circle with radius with two white circles of radius inside. This gives us an extra shaded area of . Adding these values together yields . The area of the large white circle is . Therefore, the desired fraction is .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions