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Manager  Joined: 10 Feb 2011
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Square R is inscribed in circle C and C is inscribed in  [#permalink]

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Difficulty:   85% (hard)

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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Joined: 02 Sep 2009
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Re: Square R is inscribed in circle C and C is inscribed in  [#permalink]

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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.

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