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16 Sep 2014, 00:46
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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. \(\sqrt{3}\)
A. \(\frac{1}{\sqrt{2}}\)
B. \(2\sqrt{3}\)
C. \(1\)
D. \(\sqrt{2}\)
E. \(\sqrt{3}\)
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.
Answer: C
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
14 Dec 2015, 13:56
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could you please elaborate further on how you got the answer?
