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smc

geometry senior

Problem

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.
problem
(A)
(B)
(C)
(D)
Solution
The outer circle has radius , and thus area . The little circles have area each; since there are 7, their total area is . Thus, our answer is .
Final answer
C