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Square A is inscribed inside Circle B which is then inscribed inside S

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Square A is inscribed inside Circle B which is then inscribed inside S  [#permalink]

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New post 21 Feb 2017, 05:21
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Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is 1, what is the ratio of the area of Square A to the area of Square C?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4

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Re: Square A is inscribed inside Circle B which is then inscribed inside S  [#permalink]

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New post 21 Feb 2017, 05:41
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Bunuel wrote:
Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is 1, what is the ratio of the area of Square A to the area of Square C?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4



Please check the solution as attached.

Answer: Option C
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Square A is inscribed inside Circle B which is then inscribed inside S  [#permalink]

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New post 21 Feb 2017, 07:40
Bunuel wrote:
Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is 1, what is the ratio of the area of Square A to the area of Square C?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4


Diagonal of Square A = Diameter = \(a\sqrt{2}\)

\(Radius = \frac{Diameter}{2}= (\frac{1}{2})*a\sqrt{2}=1\)

\(a\sqrt{2}=2\)

\(a=\frac{2}{\sqrt{2}}=\sqrt{\frac{4}{2}}=\sqrt{2}\)

Area of Square A \(= a^2=(\sqrt{2})^{2}=2\)

Area of Square C \(= (2)(2)=4\)

Area of Square A : Area of Square C \(= 2:4 = 1:2\)

Answer = C
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Re: Square A is inscribed inside Circle B which is then inscribed inside S  [#permalink]

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New post 23 Feb 2017, 10:48
Bunuel wrote:
Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is 1, what is the ratio of the area of Square A to the area of Square C?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4


We can first draw a diagram of what is described in the question stem.

Image

We see that the blue line represents the diagonal of square A and the diameter of circle B, and the red line also represents the diameter of circle B, but also the side of square C.

Since the radius of circle B is 1, the diameter is 2.

We then know that the diagonal of square A is also 2 and the side of square C is 2.

Since the diagonal of a square = side√2, we can create the following equation:

2 = side√2

2/√2 = side

Multiplying 2/√2 by (√2/√2), we have:

(2√2)/2 = √2

Since area of a square = side^2, the area of square A = (√2)^2 = 2 and the area of square C is 2^2 = 4.

Thus, the ratio of the area of square A to the area of square C is 2/4 = 1/2.

Answer: C
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Re: Square A is inscribed inside Circle B which is then inscribed inside S &nbs [#permalink] 23 Feb 2017, 10:48
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