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Math Help - geometry question

  1. #1
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    geometry question

    Given unit circle P. Points A and B are on the circle (r=1), forming an acute angle APB (theta). What line segment is equal to the tangent theta if line segment DC is tanget to circle at point b.
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  2. #2
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    Re: geometry question

    Hello, Pat722!

    The directions are somewhat fuzzy.
    I may have misinterpreted them.


    \text{Given unit circle }P\text{, points }A,B\text{ are on the circle, forming}
    \text{acute angle }AP\!B \,=\,\theta.\;\text{What line segment is equal to }\tan\theta
    \text{if line segment }DC\text{ is tangent to circle at point }B\,?

    I believe the diagram looks like this:
    Code:
                              E
                              o
                             .:
                            . :
                           .  :
                  * * *  A.   :
              *          o    o D
            *           /   * |
           *         1 /     *|
                      /       |
          *          / @      *
          *         o - - - - o B
          *       P      1    *
                              |
           *                 *|
            *               * |
              *           *   o
                  * * *       C
    We have the unit circle with center P and radii P\!A = PB = 1.
    \theta \,=\,\angle AP\!B,\;\theta \,<\,90^o
    CD is tangent to the circle at B.
    Extend CD to meet P\!A extended at E.

    Then: . \tan\theta \,=\,\frac{EB}{1}

    Therefore: . EB \:=\:\tan\theta
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