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Math Help - Radius of Circle #2

  1. #1
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    Radius of Circle #2

    Each of two tangents from an external point to a circle is 3cm long. The smaller arc which they intercept is 112degrees 30' 26''. Find the radius of the circle.

    Help please, I really have no idea. Can you show it with illustrations, thanks!
    Last edited by mr fantastic; February 16th 2010 at 04:12 AM. Reason: Edited post title
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  2. #2
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    Hello, reiward!

    Each of two tangents from an external point to a circle is 3 cm long.
    The smaller arc which they intercept is 112 30' 26''.
    Find the radius of the circle.
    Code:
                  * * *
              *           *   A
            *               o
           *          r   *  * *    3
                        *         *
          *           * θ     *      *
          *       C o - - - - * - - - - o P
          *           *       *      *
                        *         *
           *          r   *  * *    3
            *               o
              *           *   B
                    * * *

    The center of the circle is C; its radius is r.

    Tangents PA = PB = 3
    \angle ACB \,=\,112^o30'13'' \quad\Rightarrow\quad \theta \:=\:\angle ACP \:\approx\:56.2536^o

    In right triangle CAP\!:\;\;\sin\theta \:=\:\frac{3}{r} \quad\Rightarrow\quad r \:=\:\frac{3}{\sin\theta}

    ThereforeL . r \:=\:\frac{3}{\sin56.2536^o} \;\approx\;3.6\text{ cm}

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