circle square area ratio

[undvaulter]

If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

Π/12

Π/6

Π/2

2/Π

sqrt12Π

[ps63739]

Let area of circle A = pie*x^2
Area of circle B = 3pie*x^2
Area of square = 18pie*x^2, side of square = 3x*sqrt(2*pie) (Which is diamater for the circle inscribed in square)
Area of the circle in square = pie*(9/4)*2*pie*x^2

Ratio = (3piex^2)/((pie^2*9/2)x^2)

[thoppae.saravanan]

ACA = Area of Circle A
ACB = Area of Circle B
AS = Area of square WXYZ
ACS = Area of circle inscribed in square WXYZ

Given, ACA = 3 ACB and ACB=AS/6.

Let the radius of ACS = r.

Then, AS = 4r^2 => ACB = 2r^2/3 => ACA = 2r^2.

So ACS/ACA = pi*r^2/2r^2 = pi/2. Option C should be the answer.

OA please.

[undvaulter]

OA is Pi/2

thanks thoppae

[Ben Ku]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.