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# M12-15

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
M12-15  [#permalink]

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15 Sep 2014, 23:46
2
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Difficulty:

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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Re M12-15  [#permalink]

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15 Sep 2014, 23:46
1
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.

Answer: C
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Re: M12-15  [#permalink]

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14 Dec 2015, 12:56
could you please elaborate further on how you got the answer?
Math Expert
Joined: 02 Sep 2009
Posts: 51185
Re: M12-15  [#permalink]

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17 Dec 2015, 08:21
rhio wrote:
could you please elaborate further on how you got the answer?

Please be a little bit more specific. Thank you.
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Joined: 17 Oct 2015
Posts: 22
Concentration: Technology, Leadership
Re: M12-15  [#permalink]

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10 Jan 2016, 10:47
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:
could you please elaborate further on how you got the answer?

Please be a little bit more specific. Thank you.
Math Expert
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Posts: 51185
Re: M12-15  [#permalink]

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10 Jan 2016, 12:31
1
mestrec wrote:
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:
could you please elaborate further on how you got the answer?

Please be a little bit more specific. Thank you.

Check here: a-regular-hexagon-is-inscribed-in-a-circle-if-the-radius-of-the-circl-75199.html
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Re: M12-15  [#permalink]

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15 Jan 2016, 08:52
1
mestrec wrote:
Could you please explain why the other 2 angles are also 60?

Bunuel wrote:
rhio wrote:
could you please elaborate further on how you got the answer?

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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: M12-15  [#permalink]

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

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