Problem:
The vertices of a right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of these circles?
Answer Choices:
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B.
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E.
Solution:
Let , and be the radii of the circles centered at , and , respectively. Then , and , from which , and . Thus the sum of the areas of the circles is
The problems on this page are the property of the MAA's American Mathematics Competitions