SOLUTION: A,regular octagon of side 6cm is inscribed in acircle.calculate the diameter of the circle

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Question 1083252: A,regular octagon of side 6cm is inscribed in acircle.calculate the diameter of the circle
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
1.  Make a sketch.

    Draw the apothem in the regular octagon.

2.  The central angle is  =  = 45 degs.

    The acute angle in the right-angled triangle is  =  = 22.5 degrees.


    From the right-angled triangle, you have  = ,   or

    R = .


    You can find  using your calculator or using the formula

     = .

See the lessons
    - The side length of a regular polygon via the radius of the circumscribed circle
and
    - Miscellaneous Trigonometry problems
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