Problem:
A square has sides of length , and a circle centered at one of its vertices has radius . What is the area of the union of the regions enclosed by the square and the circle?
Answer Choices:
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Solution:
The areas of the regions enclosed by the square and the circle are and , respectively. One quarter of the second region is also included in the first, so the area of the union is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions