Question 346572: A regular hexagon is inscribed in a circle . if the perimeter of the hexagon is 54, find the circumference of the circle in terms of pi ?
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! To find the cirmcuferece of the circle (2*pi*r) we need to know the radius, r
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you have a regular hexagon
This means a 6 sided figure with all sides of equal length
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Its inscribed in a circle, so its inside the circle
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I has six central angles formed from the center of the circle to its vertices
each at 360/6=60 degrees
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The six triangles formed each with a central angle of 60 degrees
The two legs of the triangle are the radius of the cirlce and thus are equal, so the base angles are equal, but since the central angle is 60, then the base angles are 120/2=60, so the triangles are equilateral triangles, which means all sides are equal. There fore all sides of each triangle is 9 which means the radius is 9
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therfore circumference of the circle = 2*pi*9=18*pi
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