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GRE Math Challenge #18- vertex Q of square OPQR is on circle

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sandy
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GRE Math Challenge #18- vertex Q of square OPQR is on circle [#permalink] New post   07 Sep 2014, 06:31
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In the figure, vertex Q of square OPQR is on circle with centre O. If the area of the square is 8, what is the area of the circle?



A. \(8 \pi\)

B. \(8 \sqrt{2} \pi\)

C. \(16 \pi\)

D. \(32 \pi\)

E. \(64 \pi\)
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C
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Re: GRE Math Challenge #18 [#permalink] New post   09 Sep 2014, 21:59
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OQ is the diagonal of the square and the radius of the circle.

Area of square = 8 sq. units => side of square = 2*sqrt2
=> diagonal of square = sqrt2 * side = 2*2 = 4 units = OQ
Area of circle = (radius)^2*pi = (4^2)pi = 16 pi
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Re: GRE Math Challenge #18- vertex Q of square OPQR is on circle [#permalink] New post   15 Dec 2021, 03:18
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Re: GRE Math Challenge #18- vertex Q of square OPQR is on circle [#permalink]
15 Dec 2021, 03:18
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