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Square S is inscribed in circle T. If the perimeter of S is 24, what i

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Bunuel
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Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  17 Jun 2019, 23:50
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Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  18 Jun 2019, 00:14
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Bunuel wrote:
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π


The length of side of square = 24/4=6. length of the diagonal of the square = square root 2 * Side = 6*root2. Diagonal of the square must me the diameter of the circle.
So 2*pi*r=6*root2*pi .IMO Option D
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  18 Jun 2019, 01:48
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Bunuel wrote:
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π


perimeter = 24 ; each side is 6 and diagonal = diameter= 6√2
radius ; 3√2
and circumference ; 2*3√2*pi
IMO D; 6√2*π
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Abhishek009
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  15 Oct 2019, 08:31
Bunuel wrote:
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π


4s = 24

So, s = 6 ( Each side of the square is 6 )

Now, Diagonal of the Square = Diamter of the Circle

So, \(6\sqrt{2}\)= Diameter of the Circle

Now, Circumference of the Circle is π*Diamter of the Circle = 6√2*π , Answer must be (D)
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  15 Oct 2019, 15:16
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Bunuel wrote:
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π


The square is inside the circle, see attachment below. Then the length of the square is longer than the radius of the circle. Radius = 6 / sqrt(2) = 3*sqrt(2), and the circumference is 2pi * 3sqrt(2). Thus the answer is D.
Attachments

square in circle.png
square in circle.png [ 38.18 KiB | Viewed 6816 times ]


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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  16 Oct 2019, 19:21
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Bunuel wrote:
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π
B. 12π
C. 3√2*π
D. 6√2*π
E. 12√2*π


Since the perimeter of S is 24, each side is 6, and the diagonal of S = the diameter of T = 6√2. Thus, the circumference of T is 6√2*π.

Answer: D
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink] New post  16 Apr 2022, 10:11
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what i [#permalink]
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