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

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A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  28 Jan 2009, 15:44
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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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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  28 Jan 2009, 18:42
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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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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  28 Jan 2009, 19:21
agree with 1.

Same explantion as GMATTIGER's.

good picture.
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  28 Jan 2009, 19:29
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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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  29 Jan 2009, 09:48
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  13 Feb 2014, 06:42
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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  30 Apr 2014, 08:29
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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Re: A regular hexagon is inscribed in a circle. If the radius of the circl [#permalink]  29 Dec 2015, 13:06
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] 29 Dec 2015, 13:06
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