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

Question

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}

GMAT TIGER · Accepted Answer

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.

x2suresh · Answer

agree with 1.

Same explantion as GMATTIGER's.

good picture.

alpha_plus_gamma · Answer

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.

bigfernhead · Answer

Great pic and great answer(s).

jlgdr · Answer

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

hdwnkr · Answer

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

HKD1710 · Answer

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).

Sri07 · Answer

Can some one tell me what is the level of this question 500?

Bunuel · Answer

You can check the difficulty level of a question in the tags just above the first post. You can also check the stats in the original post. For this question the difficulty level is sub-600.

nkme2007 · Answer

For a regular hexagon inscribed in a circle, each side holds an angle of 60 degrees at centre of the circle.

Making the radius the other two sides of an equilateral triangle formed with the side of that regular hexagon.

Hence, the length of the side = length of the radius.

So, OA: C

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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