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Math Help - star inscribed in a circle

  1. #1
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    star inscribed in a circle

    I am trying to answer this problem as a practice for an exam and I can't seem to find the correct answer.

    In a circle with a diameter of 10m, a regular five pointed star touching its circumference is inscribed.What is the area of the part not covered by the star.

    Please help me solve this.I need the answer asap.
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  2. #2
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    Quote Originally Posted by hven191 View Post
    I am trying to answer this problem as a practice for an exam and I can't seem to find the correct answer.

    In a circle with a diameter of 10m, a regular five pointed star touching its circumference is inscribed.What is the area of the part not covered by the star.

    Please help me solve this.I need the answer asap.
    Do you mean a pentagram? (See attachment)

    The radius is divided into 2 parts by an inner vertex:

    \dfrac{red}{blue} = \dfrac{blue}{red+blue}

    which is nothing but the golden ratio.
    Attached Thumbnails Attached Thumbnails star inscribed in a circle-aussen_pentagon.png  
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  3. #3
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    Thanks for the help earboth! It really helped me a lot!
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