A circle is circumscribed around a square and inscribed in a : PS Archive
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# A circle is circumscribed around a square and inscribed in a

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A circle is circumscribed around a square and inscribed in a [#permalink]

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19 Sep 2006, 12:46
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A circle is circumscribed around a square and inscribed in a larger square. A point inside the larger square is chosen at random. Which of the following best approximates the probability that this point is inside the circle but outside the square inscribed in the circle?

(A) 28% (B) 31% (C) 35% (D) 39% (E) 43%
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19 Sep 2006, 12:58
A. 28%

Let side of inner square = a
Area of inner square = a^2

Diameter of circle = a x sqrt(2)
Radius = a x sqrt(2) /2

Area of circle = pi x a^2/2 = 22a^2/7x2 = 11a^2/7

Area of circle not part of inner square = 11a^2/7 - a^2 = 4a^2/7

Side of outer Square = diameter of circle = a x sqrt(2) = 2a^2

Prob(Success) = Area of inner circle not part of Square/Area of outer square
= (4a^2/7)/(2a^2) = 2/7 = 28.5%

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19 Sep 2006, 21:57
Infact the exact answer will be 28.56...%
_________________

Last edited by cicerone on 25 Sep 2008, 00:24, edited 1 time in total.
19 Sep 2006, 21:57
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