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SAT I 一日一问：2013年3月15日

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The Correct answer is C.

Explanation

Segment line C D is a radius of the large semicircle, and it is also a diameter of the shaded circle, so the radius of the large semicircle is equal to twice the radius of the shaded circle. Let be the radius of the shaded circle. Then 2 times r is the radius of the large semicircle, and so the area of the semicircle is (pi times (2 times r)^2) over 2 = (4 times pi times r^2) over 2 = 2 times pi times r^2 . This area is given as , and so the area of the shaded circle is (pi times r^2) = (2 times pi times r^2) over 2 = 24 over 2 = 12 .