Difference between revisions of "2003 AMC 10B Problems/Problem 19"
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Revision as of 11:10, 4 July 2013
Contents
[hide]Problem
Problem 19
Three semicircles of radius are constructed on diameter of a semicircle of radius . The centers of the small semicircles divide into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?
Solution
By drawing four lines from the intersect of the semicircles to their centers, we have split the white region into of a circle with radius and two equilateral triangles with side length . This gives the area of the white region as . The area of the shaded region is the area of the white region subtracted from the area of the large semicircle. This is equivalent to .
Thus the answer is .
See Also
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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