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In the above figure, the two circles are tangential to l and

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by Max@Math Revolution » Fri Aug 23, 2019 12:28 am
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[GMAT math practice question]

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In the above figure, the two circles are tangential to l and m. The area of A and that of B are the same. What is the value of x?

A. π
B. 2Ï€
C. 3Ï€
D. 4Ï€
E. 6Ï€
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by Max@Math Revolution » Sun Aug 25, 2019 5:36 pm
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When we calculate the sum of the areas of sectors OPQ and O’RS, the area B is double-counted. Since A and B have equal areas, the sum of the areas of sectors OPQ and O’RS is the same as the area of the rectangle OPSO’. Note that both sectors have the same area.

The rectangle OPSO’ has sides of length x and 6, so its area is 6x. As this area is twice the area of sector OPQ, which has a central angle of 90° and a radius of 6, we have
6x = 2*(π*6^2*(1/4)) and 6x = 18π.
Thus, x = 3π.

Therefore, the answer is C.
Answer: C
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