Problem:
A circle of radius is surrounded by circles of radius as shown. What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Construct the square by connecting the centers of the large circles, as shown, and consider the isosceles right .
Since and , we have . So
Applying the quadratic formula gives .
The problems on this page are the property of the MAA's American Mathematics Competitions