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# M12-15

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Math Expert
Joined: 02 Sep 2009
Posts: 56306

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16 Sep 2014, 00:46
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15% (low)

Question Stats:

81% (00:53) correct 19% (00:54) wrong based on 79 sessions

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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. $$\sqrt{3}$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:46
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Official Solution:

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. $$\sqrt{3}$$

Connect the center of the circle with each of the hexagon's vertices to get six triangles. In each triangle, the angle at the center is 60 degrees $$(\frac{360}{6})$$. The two other angles are also 60 degrees each. Thus, all six triangles are equilateral.

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Joined: 25 Apr 2015
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14 Dec 2015, 13:56
Math Expert
Joined: 02 Sep 2009
Posts: 56306

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17 Dec 2015, 09:21
rhio wrote:

Please be a little bit more specific. Thank you.
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Joined: 17 Oct 2015
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10 Jan 2016, 11:47
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:

Please be a little bit more specific. Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 56306

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10 Jan 2016, 13:31
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mestrec wrote:
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:

Please be a little bit more specific. Thank you.

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15 Jan 2016, 09:52
1
mestrec wrote:
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:

Please be a little bit more specific. Thank you.

Hi,
hexagon as shown is inscribed in the circle..
each angle of hexagon is 120...
when you join opposite vertices, these are also the diagonals and bisect the angles 120..

this is the reason why all three angles are 60 and teh side of hexa too equals radius =1..
hope it helps
>> !!!

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Joined: 10 Sep 2014
Posts: 78
GPA: 3.5
WE: Project Management (Manufacturing)

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25 Mar 2018, 21:20
1
Bunuel We really needed a picture with this question. could not anticipate anything without a pic.
Re: M12-15   [#permalink] 25 Mar 2018, 21:20
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# M12-15

Moderators: chetan2u, Bunuel