2002 AMC 10B Problems/Problem 5
Problem
Circles of radius and are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.
Solution
A line going through the centers of the two smaller circles also goes through the diameter. The length of this line within the circle is Because this is the length of the larger circle's diameter, the length of its radius is
The area of the large circle is , and the area of the two smaller circles is To find the area of the shaded region, subtract the area of the two smaller circles from the area of the large circle.
See Also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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