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# A square is inscribed in a circle. What is the area of the circle?

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A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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17 Apr 2018, 05:45
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A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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17 Apr 2018, 10:28
IMO D
if a square is inscribed in a circle then the diagonal of the square is also the diameter of the circle. If we know the value of one we can find the other

Statement (1)- area of the square is given. From this we can find the diagonal of square and hence the radius of the circle. Thus area of the circle can be known. Hence sufficient

Statement(2)-Radius can be known from this and hence the area of the circle. Sufficient

Hence D

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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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18 Apr 2018, 05:27
Bunuel wrote:
A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

We are given that square is inscribed in a circle, but we dont know whether its the largest possible square inscribed in that circle or not.
To solve this question, we need to know the radius of this circle.

(1) Area of square = side*side = 18. So side of square can be found but we dont know whether its the largest possible square which can be inscribed in this circle, so we cannot apply the relation that diagonal of this square = diameter of this circle. So we cannot find the diameter or the radius of this circle. So not sufficient.

(2) Circumference is given, so we can find the radius, and can thus find the area. Sufficient.

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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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18 Apr 2018, 05:43
Only a unique square can be inscribed in a circle. It is also the largest rectangle possible inscribed in a circle.

Hence statement 1 is sufficient.

Answer shall be D.

amanvermagmat wrote:
Bunuel wrote:
A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

We are given that square is inscribed in a circle, but we dont know whether its the largest possible square inscribed in that circle or not.
To solve this question, we need to know the radius of this circle.

(1) Area of square = side*side = 18. So side of square can be found but we dont know whether its the largest possible square which can be inscribed in this circle, so we cannot apply the relation that diagonal of this square = diameter of this circle. So we cannot find the diameter or the radius of this circle. So not sufficient.

(2) Circumference is given, so we can find the radius, and can thus find the area. Sufficient.

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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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08 Jul 2018, 17:08
amanvermagmat wrote:
Bunuel wrote:
A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

We are given that square is inscribed in a circle, but we dont know whether its the largest possible square inscribed in that circle or not.
To solve this question, we need to know the radius of this circle.

(1) Area of square = side*side = 18. So side of square can be found but we dont know whether its the largest possible square which can be inscribed in this circle, so we cannot apply the relation that diagonal of this square = diameter of this circle. So we cannot find the diameter or the radius of this circle. So not sufficient.

(2) Circumference is given, so we can find the radius, and can thus find the area. Sufficient.

Ans is D
coz area of square =d\sqrt{}2/2
d=6=2[*]reduis
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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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09 Jul 2018, 02:59
Bunuel wrote:
A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

The question asks us to find Area of the circle. Hence finding the radius of the circle is Sufficient.

Statement 1: The inscribed square has Area = 18, hence we can find its side & the diagonal.

The diagonal of the square is the diameter for the circle. Hence we can find radius.

Statement 1 alone is Sufficient.

Statement 2: Circumference = $$6\pi$$

Sufficient to find radius.

Statement 2 alone is Sufficient.

Thanks,
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Re: A square is inscribed in a circle. What is the area of the circle?  [#permalink]

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13 Jul 2018, 23:47
Bunuel wrote:
A square is inscribed in a circle. What is the area of the circle?

(1) The area of the square is 18.
(2) The circumference of the circle is $$6\pi$$.

Condition 1. a2= 18
We know when a square is circumscribed by a circle, then the area of the circle is pi/2*a2 (where a is the length of sides of the square).
So, sufficient,

Condition2, 2*pi*r=6, so, we can clearly get the area.
Sufficient.

Hence, Ans- D
Re: A square is inscribed in a circle. What is the area of the circle? &nbs [#permalink] 13 Jul 2018, 23:47
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# A square is inscribed in a circle. What is the area of the circle?

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