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A square is inscibed in a circle of radius s and circumscribed about a

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A square is inscibed in a circle of radius s and circumscribed about a [#permalink]

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New post 23 Nov 2017, 22:16
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A square is inscibed in a circle of radius s and circumscribed about a circle of radius r. Which of the following is an expression for the perimeter of the square?

(A) 8s
(B) 8r
(C) 4s + 4r
(D) 2√2s + 2√2r
(E) 2s + 2r
[Reveal] Spoiler: OA

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Kudos [?]: 135629 [0], given: 12705

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Re: A square is inscibed in a circle of radius s and circumscribed about a [#permalink]

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New post 23 Nov 2017, 23:34
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From information about square is inscribed in a circle of radius s.
The diameter of the circle is 2s. The diagonal of the inscribed square is the same as the diameter of the circle that circumscribes it.
So, diagonal of square = 2s and side of square = 2s/(√2) = √2s. Hence, perimeter = 4√2s

From information about square is circumscribed about a circle of radius r
The diameter of this circle is 2r. The side of the square will be the same as the diameter of the circle inscribed in it.
So, side of square = 2r.
Perimeter of the square = 8r.

Choice B.

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Re: A square is inscibed in a circle of radius s and circumscribed about a   [#permalink] 23 Nov 2017, 23:34
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