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

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Source: — Data Sufficiency |

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by Ian Stewart » Sun Mar 31, 2019 8:31 am

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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.
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