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geometry senior
Problem
A circle with area is contained in the interior of a larger circle with area . If the radius of the larger circle is , and if is an arithmetic progression, then the radius of the smaller circle is
(A)
(B)
(C)
(D)
(E)
Solution
The area of the larger circle is . Then are in an arithmetic progression. Thus . This simplifies to , or . The radius of the smaller circle is .
Final answer
E