2010 AMC 8 Problems/Problem 23
Problem
Semicircles and pass through the center . What is the ratio of the combined areas of the two semicircles to the area of circle ?
Solution
By the Pythagorean Theorem, the radius of the larger circle turns out to be . Therefore, the area of the larger circle is . Using the coordinate plane given, we find that the radius of each of the two semicircles to be 1. So, the area of the two semicircles is . Finally, the ratio of the combined areas of the two semicircles to the area of circle is .
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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