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# A circle C is drawn around a square S such that the sides of the squar

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
A circle C is drawn around a square S such that the sides of the squar  [#permalink]

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09 Dec 2019, 00:18
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:53) correct 17% (01:27) wrong based on 23 sessions

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A circle C is drawn around a square S such that the sides of the square become the four chords of the circle. What is the area of square S?

(1) Had a circle been drawn such that the four sides of square S were tangents to the circle, the area of the circle would be 30 square centimetres less than the area of circle C

(2) Had a circle been drawn with the diagonal of square S as its radius, the area of the circle have been 180 square centimetres more than the area of circle C

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Joined: 19 Oct 2018
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Re: A circle C is drawn around a square S such that the sides of the squar  [#permalink]

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09 Dec 2019, 11:19
Let side of the square =a

Radius of the circle C= 1/2* diagonal of square= $$\frac{1}{2}*\sqrt{2}a$$

Area of circle C= $$pi*\frac{a^2}{2}$$

Statement 1-

Had a circle been drawn such that the four sides of square S were tangents to the circle, it's radius would have half of the side of the square.

($$pi*\frac{a^2}{2}$$) - ($$pi*\frac{a^2}{4}$$) = 30

We can find a^2.

Sufficient

Statement 2-

($$pi*2*a^2$$) - ($$pi*\frac{a^2}{2}$$)= 180

We can find a^2.

Sufficient

Bunuel wrote:
A circle C is drawn around a square S such that the sides of the square become the four chords of the circle. What is the area of square S?

(1) Had a circle been drawn such that the four sides of square S were tangents to the circle, the area of the circle would be 30 square centimetres less than the area of circle C

(2) Had a circle been drawn with the diagonal of square S as its radius, the area of the circle have been 180 square centimetres more than the area of circle C

Are You Up For the Challenge: 700 Level Questions
Re: A circle C is drawn around a square S such that the sides of the squar   [#permalink] 09 Dec 2019, 11:19
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