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Two squares are oriented with respect to a circle as shown in the figu

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Two squares are oriented with respect to a circle as shown in the figu  [#permalink]

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New post Updated on: 18 Feb 2019, 07:41
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Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:

Image

Image

A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2

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Originally posted by fitzpratik on 18 Feb 2019, 06:58.
Last edited by fitzpratik on 18 Feb 2019, 07:41, edited 3 times in total.
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Re: Two squares are oriented with respect to a circle as shown in the figu  [#permalink]

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New post 18 Feb 2019, 07:34
fitzpratik wrote:
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:

Image

A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2



Figure is not visible...
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Re: Two squares are oriented with respect to a circle as shown in the figu  [#permalink]

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New post 18 Feb 2019, 07:42
GMATinsight wrote:
fitzpratik wrote:
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:

Image

A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2



Figure is not visible...



Have edited the link. I hope its visible now
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Re: Two squares are oriented with respect to a circle as shown in the figu  [#permalink]

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New post 18 Feb 2019, 08:21
fitzpratik wrote:
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:

Image

Image

A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2



fitzpratik, it is visible now.

So if we consider the circle of radius 2, then the smaller square will have side as 2\(\sqrt{2}\), since it is a square so the center angle will be a \(90^0\) that will make a 45-45-90 triangle

Now the bigger square will have side as 4, since the circle's diameter = square's side

Area of smaller square / Area of bigger square = 8/16

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Re: Two squares are oriented with respect to a circle as shown in the figu  [#permalink]

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New post 18 Feb 2019, 10:28
fitzpratik wrote:
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:

Image

Image

A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2



the diameter of the circle will be equal to the side of the large square ; let it be = 4
and the diagonal of the small circle equal to diameter of circle ; so d = s√2 ; 4 =s√2 ; side of small square = 2 √2

so area of small square/ area of large square ; 2 *2 * 2 / 4 * 4 ; 1:2 IMO E
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Re: Two squares are oriented with respect to a circle as shown in the figu   [#permalink] 18 Feb 2019, 10:28
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