Problem:
Two circles of radius are centered at and at . What is the area of the intersection of the interiors of the two circles?
Answer Choices:
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B.
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E.
Solution:
The two circles intersect at and , as shown.
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Half of the region described is formed by removing an isosceles right triangle of leg length from a quarter of one of the circles. Because the quarter-circle has area and the triangle has area , the area of the region is .
The problems on this page are the property of the MAA's American Mathematics Competitions