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Square R is inscribed in circle C and C is inscribed in

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Square R is inscribed in circle C and C is inscribed in  [#permalink]

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New post 14 Feb 2011, 15:50
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Question Stats:

55% (02:19) correct 45% (02:18) wrong based on 152 sessions

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Square R is inscribed in circle C and C is inscribed in square T. Is the circumference of С greater than 10?

(1) The side length of R is greater than 2.
(2) The side length of T is greater than 4.
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Re: Square R is inscribed in circle C and C is inscribed in  [#permalink]

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New post 14 Feb 2011, 16:57
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banksy wrote:
Square R is inscribed in circle C and C is inscribed in square T. Is the circumference of С greater than 10?
(1) The side length of R is greater than 2.
(2) The side length of T is greater than 4.


There is a fixed relationship between a side of a square and the radius of inscribed circle: \(S=2r\);

Next, there is also a fixed relationship between the radius of a circle and a side of inscribed square: \((2r)^2=s^2+s^2\) --> \(s=r*\sqrt{2}\);

Question: is \(2\pi{r}>10\)? --> is \(r>\frac{5}{\pi}\approx{\frac{5}{\frac{22}{7}}}=\frac{35}{22}\approx{1.6}\)?

(1) The side length of R is greater than 2 --> \(s=r*\sqrt{2}>2\) --> \(r>\sqrt{2}\approx{1.4}\). Not sufficient.

(2) The side length of T is greater than 4 --> \(S=2r>4\) --> \(r>2\). Sufficient.

Answer: B.
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Re: Square R is inscribed in circle C and C is inscribed in  [#permalink]

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New post 17 Jan 2019, 15:22
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Re: Square R is inscribed in circle C and C is inscribed in   [#permalink] 17 Jan 2019, 15:22
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