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Circle O is inscribed within square A. Square B is

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Joined: 29 Jan 2005
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Circle O is inscribed within square A. Square B is [#permalink]  29 Oct 2005, 08:55
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Circle O is inscribed within square A. Square B is inscribed within circle O. What is the ratio of the area of square A to square B? (no diagram drawn)
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Re: PS Kaplan#9 [#permalink]  29 Oct 2005, 10:12
GMATT73 wrote:
Circle O is inscribed within square A. Square B is inscribed within circle O. What is the ratio of the area of square A to square B? (no diagram drawn)

For square A the area be a^2.

Now for circle radius be a/2 or diameter be d = a.

For inner square the diagonal be d. area will be d^2/2.

our ratio be 2:1.
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Lets take outer square to be 4x4 = area 16
circle diameter = 4
hence inner square diagonal = 4
we know it is 90 45 45. so sides are 1:1:sqrt(2)
so inner square area is (4/sqrt(2))*(4/sqrt(2)) = 16/2 = 8

Hence 2:1
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