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

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Intern
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Square S is inscribed in circle T. If the perimeter of S is 24, what  [#permalink]

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New post 20 Aug 2011, 04:29
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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√ 2π
d) 6√ 2π
e) 12√ 2π
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what  [#permalink]

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New post 20 Aug 2011, 09:16
Hmm,
The perimeter of the square is 24, so that means that the length of each side is 6
Let length of each side be a
24=4a
a=6

When they say the square is inscribed in a circle, all vertices of the square lie on the circle.
So if we join the opposite vertices of the square we basically get the diagonal of the square.
Let ABCD be the required square. BD can be a diagonal and O be the center of the circle.

Central angle is twice the inscribed angle. (Property in circles)
Join OB and OD, now BOD=2BAD
BOD=180
i.e BOD is a straight line segment therefore diagonal BD passes through the center.
this means BD is the diameter
BD^2=2*a^2
BD=6sqrt2

Now circumference=2*pi*r or pi*d where d is diameter of the circle
therefore circumference is pi*6sqrt2

Hope this helps.
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what  [#permalink]

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New post 20 Aug 2011, 15:40
1
square forms two right angled triangles.

Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.

hypotenuse here = diagonal of the square = 6 sqrt(2) = diameter
=> radius = 3 sqrt(2)

Circumference of the circle = 2pi r = 6 pi sqrt(2)

Answer is D.
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what  [#permalink]

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New post 23 Jan 2018, 22:22
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Re: Square S is inscribed in circle T. If the perimeter of S is 24, what &nbs [#permalink] 23 Jan 2018, 22:22
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