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Math Help - circle problem

  1. #1
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    circle problem

    circle problem-circlequestion.jpg

    I'm having trouble with this question. For the first part Im guessing that the radius is 2 times larger for the bigger circle and therefore its area is four times as large, but I can't seem to prove that the radius is twice as large.


    I'd appreciate it if anyone could help me out on this question
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  2. #2
    Senior Member vincisonfire's Avatar
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    If c is the length of side of triangle
    Height is  \sqrt{\frac{3}{2}} c by pythagore theorem
    Height is  r_{small} + r_{large}
    Draw a rectangle triangle which hypothenuse is   r_{large} and one of small side   r_{small}
    You find that   r_{large} = \frac{\sqrt{3} \cdot c}{3}
      r_{small} = \frac{\sqrt{3} \cdot c}{6}
    And you were right.
    Ok for the rest?
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  3. #3
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    thanks for the help.

    I'm also a bit stuck on the second part, any ideas on what to do?
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  4. #4
    Senior Member vincisonfire's Avatar
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    Of course, the first question is  \frac{4}{1} because
     A = \pi r^2 if r is twice as large than area is four time bigger.
     area_{curve triangle} = \frac{area_{triangle} - area_{small circle}}{3}
     area_{arc of circle} = \frac{area_{large circle } - area_{triangle}}{3}
    You know all you need to calculate these area with what I told you
    Answer is  \frac{2 \cdot(3\cdot\sqrt(3)-2\cdot \pi)}{\pi-6\cdot\sqrt(3)}
    Last edited by vincisonfire; October 30th 2008 at 02:18 PM.
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  5. #5
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    circle problem

    posted by david 18 and answered by vincesonfire

    this problem is simplified by taking unity as the radius of the large circle.Following vinci formulars iget an answer as follows

    3/4xradical 3-pi/4 dividedby pi-3/4 xradical 3 and numerically slightly lower than the previous answer and does not generate negative numbers




    bj
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