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# What is the circumference of circular region R? (1) The area of R is

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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
Hi Bunuel,

When we say that a square is inscribed in a circle, is it true in all cases that the 4 vertices of the square will always be on the circle? Can we have a square in which may be 3 vertices of the square are on the circle?

I know this is a very basic question, but I had made a similar mistake earlier in one of a data sufficiency question.

Thanks!!
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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
anupam87 wrote:
Hi Bunuel,

When we say that a square is inscribed in a circle, is it true in all cases that the 4 vertices of the square will always be on the circle? Can we have a square in which may be 3 vertices of the square are on the circle?

I know this is a very basic question, but I had made a similar mistake earlier in one of a data sufficiency question.

Thanks!!

A polygon is inscribed in a circle means that all of its vertices are on the circumference.
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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
To find the circumference of the circular area, we need the radius

Statement 1 - Radius can be arrived from the given value for area

36π=πr^2

Statement 2 - since the square is inscribed,
the diagnols of the square = diameter of the circular area

Using area of square, side of square can be determined.

Using side of the square, diagonal can be determined.

Using diagonal, diameter / radius of the circular area can be determined.

Hence, both statements are sufficient. IMO option D

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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
Nanobotstv wrote:
What is the circumference of circular region R?

(1) The area of R is 36 $$\pi$$

(2) The area of a square region inscribed in R is 72.

#1
r=6
suffiecient
#2
s=6√2
diagonal = diameter= 12; radius = 6
sufficeint
IMO D
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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
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Re: What is the circumference of circular region R? (1) The area of R is [#permalink]
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