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Thread: Arcs

  1. #1
    Junior Member
    Joined
    Jun 2010
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    Arcs

    Please give me full solution of this question with image also:
    If X and Y are the middle points of arcs AB and CD of circle and sigment joining by X and Y cuts the AB and CD at point P and Q then prove that AP=AQ
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  2. #2
    Super Member

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    Hello, soni!

    There must be a typo . . . The problem makes no sense.


    $\displaystyle X\text{ and }Y$ are midpoints of arcs $\displaystyle AB\text{ and }CD$ of a circle
    and segment $\displaystyle XY$ cuts chords $\displaystyle AB\text{ and }CD$ at $\displaystyle P\text{ and }Q$, resp.

    Prove: .$\displaystyle AP=AQ$ . ??
    Code:
                      C
              A   * * o
              o       |   *
            * |       |     *
           *  |       |      *
              |       |
          *   |P      |Q      *
        X o - + - - - + - - - o Y
          *   |       |       *
              |       |
           *  |       |      *
            * |       |     *
              o       |   *
              B   * * o
                      D

    Draw segment $\displaystyle AQ.$

    We can see that $\displaystyle AP$ is never equal to $\displaystyle AQ.$
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