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Inscribing a quadrilateral in a circle

  1. Aug 1, 2007 #1
    1. The problem statement, all variables and given/known data

    If both pairs of opposite angles of a quadrilateral add up to 180, is it always possible to inscribe it in a circle?


    2. Relevant equations



    3. The attempt at a solution

    The converse is easily proven, since the angle between two chords standing on the circumfrence is half of the corresponding central angle.
     
  2. jcsd
  3. Aug 1, 2007 #2
    If by inscribe, you mean that all four vertices lie on the circle, I dont think so.
     
  4. Aug 1, 2007 #3

    Dick

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    It is true. Draw the circle containing three points of the quadrilateral and then use the supplementary angle property to show the fourth point must lie on the circle.
     
  5. Aug 1, 2007 #4
    Yes, but if only two points lie on the circle, then the other two dont necessarily have to. Thats what I was thinking about. The same obviously goes for one point lying on the circle.

    In any case, the opposite angles of a quadrilateral will always be supplementary.
     
  6. Aug 1, 2007 #5
    No, e.g. a diamond.
     
  7. Aug 1, 2007 #6

    Dick

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    You can put a circle through any three noncollinear points.
     
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