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A regular hexagon is inscribed in a circle. If the radius of the circl

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New post 28 Jan 2009, 16:44
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A regular hexagon is inscribed in a circle. If the radius of the circle is 1, what is the length of the side of the hexagon? (A hexagon is a six-sided polygon).

A. \(\frac{1}{\sqrt{2}}\)
B. \(2\sqrt{3}\)
C. \(1\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
[Reveal] Spoiler: OA
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bigfernhead wrote:
Regular hexagon is inscribed in a circle. If the radius of the circle is 1, what is the length of the side of the hexagon? (Hexagon is a six-side polygon)


Since the hexagon is a regular one, the side should be equal to redius or 1.

Draw lines from center to the edges of a given side, AB. Doing so would create a 60 degree angle at the center. Since the sides AO and BO are equal to redius, the angles BAO and ABO are also equal. They each are also 60 degree. So the triangle becomes equilateral. Therefore the side AB is also 1.
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New post 28 Jan 2009, 20:21
agree with 1.

Same explantion as GMATTIGER's.

good picture.
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New post 28 Jan 2009, 20:29
Just to nitpick GT's solution.

sum of angles of hexagon=(6-2)*180 = 720
shared by 6 equal angles = so each angle = 720/6 = 120

this angle will be split in 2 eqaul parts by a line joining center of circle to point forming angle. making the triangle thus formed an equilateral triangle.
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New post 29 Jan 2009, 10:48
Great pic and great answer(s).
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]

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New post 30 Apr 2014, 09:29
Here let's put some answer choices on this question to make it more realistic

A. 1
B. sqrt (2)
C. sqrt (3)
D. 2 sqrt (2)
E. 1/2
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New post 29 Dec 2015, 14:06
Sum of interior angles of a polygon = 360 degree

A regular polygon could be divided into 6 equal areas. Also each of them would be equilateral. Since radius is one of the sides. Each side = 1
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]

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New post 09 Apr 2016, 10:36
bigfernhead wrote:
A regular hexagon is inscribed in a circle. If the radius of the circle is 1, what is the length of the side of the hexagon? (A hexagon is a six-sided polygon).

A. \(\frac{1}{\sqrt{2}}\)
B. \(2\sqrt{3}\)
C. \(1\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)


formula to calculate the angle b/w any two side of polygon = ((n-2) * 180) / n
for hexagon it is = 720/6 is 120.

Now that it is regular, a line from any vertex to centre of the circle will divide the angle in half. and the triangle made by joining the centre of circle with two vertex of hexagon will be equilateral.

Hence the side will be 1 (equal to radius).
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl   [#permalink] 09 Apr 2016, 10:36
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