If the red area equals the blue area, what is the value of: (large cir

Question

https://gmatclub.com/forum/download/file.php?id=55324 If the red area (between a square and is inscribed circle) equals the blue area (between a smaller circle and is inscribed square) , what is the value of: (large circle's radius)/(small circle's radius)? A. \sqrt{\frac{\pi - 4}{4 - \pi}} B. \sqrt{\frac{\pi - 3}{4 - \pi}} C. \sqrt{\frac{\pi - 2}{4 - \pi}} D. \sqrt{\frac{\pi - 2}{5 - \pi}} E. \sqrt{\frac{\pi - 2}{6 - \pi}} Are You Up For the Challenge: 700 Level Questions 2020-06-15_2159.png

RaghavKhanna · Answer

Let the radius of bigger circle = R
And,
The radius of smaller circle = r

=>  Side of bigger square = 2R 
And,
Side of smaller square = x 
=> x^2 = r^2 + r^2
=>  x = r*root(2)

Now,

Area of red region = Area of the bigger square - Area of the bigger circle 
=> Area of the red region = 4R^2 - pi * R^2

And,
 Area of blue region = Area of smaller circle - Area of smaller square 
=> Area of blue region = pi * r^2 - 2*r^2

According to the question: 
4R^2 - pi*R^2 = pi*r^2 - 2*r^2
=>R^2 / r^2 = pi - 2 / 4 - pi

=>  R/r = root

=>  Answer: C

Babineaux · Answer

Please refer to the attached pic

IMO ans is C

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yashikaaggarwal · Answer

Let Side of outer square be 2x, which is also the Diameter of outer Circle 
So the radius of outer Circle= 2x/2 = x
Area of red zone = Area of Outer Square - Area of outer Circle 
RedZone = (2x)^2-π(x)^2
RedZone = 4x^2-π(x^2) ---------(1)

Let Diagonal of inner square be 2y, which is also the Diameter of inner Circle 
So the radius of outer Circle= 2y/2 = y
Side of inner square = (2y)^2=2(S)^2
4y^2 = 2(S^2)
2y^2 = S^2
√2y = S {inner square side}
Area of Blue zone = Area of Inner Circle - Area of inner Square 
BlueZone = πy^2-2Y^2
BlueZine = y^2π-2y^2 ---------(2)

y^2π - 2y^2 = 4x^2 - π(x^2)
Y^2(π-2) = x^2(4-π)
π-2/4-π = x^2/y^2
Taking square root
√π-2/4-π = √x^2/y^2
√π-2/4-π = x/y

Answer is C

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ScottTargetTestPrep · Answer

Solution:
 
We can let the side length of the larger square (or the diameter of the larger circle) be 2 and the radius of the smaller circle be r. Thus, the side length of the smaller square is r√2, notice, too, that the radius of the larger circle is 1. We can create the equation:

red area = blue area

2^2 - π * 1^2 = π * r^2 - (r√2)^2

4 - π = πr^2 - 2r^2

4 - π = r^2(π - 2)

r^2 =(4 - π)/(π - 2)

r = √

So the radius of the smaller circle is √ . Since the radius of the larger circle is 1, therefore, the value of (large circle’s radius)/(small circle’s radius) is:

1 / √  = √

Answer: C

If the red area equals the blue area, what is the value of: (large cir

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If the red area equals the blue area, what is the value of: (large cir

Prep Toolkit

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My Rewards