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Geometry

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A regular hexagon is circumscribed about the ring surrounding the clock face. The diameter of the ring is 10in. Find the perimeter if the clock face.

Please included work/steps to solve. Thanks!

  • Geometry - ,

    I assume that you want the perimeter of the hexagon, since the perimeter of the circle would be real easy.
    From the centre sketch one of the six isosceles triangles that make up the hexagon.
    Draw in the height, which would be 5 inches.
    the central angle is 60°
    The height creates a 30-60-90 triangle, and we can find the shortest side of that right-angled triangle using simple ratios of 1:√3:2
    x/5 = 1/√3
    x = 5/√3
    so each side of the hexagon is 10√3
    and the perimeter would be 60/√3 or 20√3 after rationalizing.

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