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Math Help - In quadrilateral, prove sum of angles AOB and COD =180...?

  1. #1
    Super Member fardeen_gen's Avatar
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    In quadrilateral, prove sum of angles AOB and COD =180...?

    Let ABCD be quadrilateral inscribed in a circle with center O. Prove that sum of the angles AOB and COD = 180.
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  2. #2
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    Hello, fardeen_gen!

    Is there a typo ... or omitted information?
    . . The statement is not true . . .


    Let ABCD be a quadrilateral inscribed in a circle with center O.
    Prove that: . \angle AOB + \angle COD \:= \:180^o
    Counter-example . . .
    Code:
              A   * * *   B
              o           o
            *   \       /   *
           *     \     /     *
                  \   /
          *        \ /        *
          *         *O        *
          *        / \        *
                  /   \
           *     /     \     *
            *   /       \   *
              o           o
              D   * * *   C

    For the statement to be true,
    . . AC and BD must be perpendicular diameters ... always!

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  3. #3
    Super Member fardeen_gen's Avatar
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    I posted the question as it was given in the source. Thanks for the counter example.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by fardeen_gen View Post
    Let ABCD be quadrilateral inscribed in a circle with center O. Prove that sum of the angles AOB and COD = 180.
    Its not true, since angle AOB can be changed without altering angle COD their angle sum cannot be an invariant of a cyclic quadrilateral.

    RonL
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