Problem:
An annulus is the region between two concentric circles. The concentric circles in the figure have radii and , with . Let be a radius of the larger circle, let be tangent to the smaller circle at , and let be the radius of the larger circle that contains . Let , and . What is the area of the annulus?
Answer Choices:
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Solution:
The area of the annulus is the difference between the areas of the two circles, which is . Because the tangent is perpendicular to the radius , , so the area is .
The problems on this page are the property of the MAA's American Mathematics Competitions