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.

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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