ΒΆ 2010 AMC8 Problem 23
Problem:
Semicircles and pass through the center of circle . What is the ratio of the combined areas of the two semicircles to the area of the circle
Answer Choices:
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B.
C.
D.
E.
Solution:
By the Pythagorean Theorem, the radius of circle is . Given the coordinates , and , the diameters and of the semicircles have length . So the areas of the two semicircles will equal the area of a circle of radius . Thus the desired ratio is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions