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

Question

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

GMATinsight · Answer

Please check the solution as attached.

Answer: Option C

BillyZ · Answer

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

ScottTargetTestPrep · Answer

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

https://i.imgur.com/Pso4pJs.png

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

bumpbot · Answer

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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

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