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]

14 Feb 2011, 15:50

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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]

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] 14 Feb 2011, 16:57

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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

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

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