OG Square ABCD is inscribed in circle O

Hi AbeNeedsAnswers,

We're told that Square ABCD is inscribed in circle O. We're asked for the AREA of square region ABCD. This is a great 'concept question', meaning that you don't have to do any math to answer it as long as you recognize the concepts involved. Since the square is INSCRIBED in the circle, the DIAGONAL of the square is EQUAL to the DIAMETER of the circle (and by extension, HALF the diagonal of the square is equal to the RADIUS of the circle). Thus, to answer the question, we just need to know the radius of the circle....

1) The AREA of circular region O is 64Ï€.

Since the area of the circle = 64Ï€ = (R^2)Ï€, the radius = 8 and we CAN answer the question (we don't actually have to calculate the area though to know that there will be just one answer to the question.
Fact 1 is SUFFICIENT

2) The CIRCUMFERENCE of circle O is 16Ï€.

Since the circumference of the circle = 16Ï€ = (2)(R)Ï€, the radius = 8 and we CAN answer the question (we don't actually have to calculate the area though to know that there will be just one answer to the question.
Fact 2 is SUFFICIENT

Final Answer: D

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