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In the diagram above, O is the center of the circle and ACDE

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by BTGmoderatorDC » Thu Mar 28, 2019 4:48 am

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In the diagram above, O is the center of the circle and ACDE is a square. What is the area of the square?


(1) the circle has a radius of 2

(2) angle ACB = 90°

OA A

Source: Magoosh
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Source: — Data Sufficiency |

by Ian Stewart » Sun Mar 31, 2019 8:31 am
If you connect a diameter of a circle to a point C on the circle, you always form a right angle at C, so Statement 2 tells us nothing new, and is useless. Using only Statement 1, since we know we have a right triangle, and we know two of its sides (the hypotenuse is twice the radius, so is 4), we can find the third side using Pythagoras, and since that gives us one side of the square, we can find the square's area. So Statement 1 is sufficient alone and the answer is A.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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