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Question

Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region. Express your answer in terms of . FIGURE

Accepted Answer

The diameter of the large circle is 6+4=10, so its radius is 5. Hence, the area of the shaded region is (5^2)-(3^2)-(2^2)=(25-9-4)=12.