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Math Help - guadrilateral inscribed in a circle...

  1. #1
    mdk
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    guadrilateral inscribed in a circle...

    If a quadrilateral ABCD is inscribed in a circle, then the opposite angles of the quadrilateral are supplementary.

    I'm not sure how to write this proof. Any help would be greatly appreciated!
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  2. #2
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    Quote Originally Posted by mdk View Post
    If a quadrilateral ABCD is inscribed in a circle, then the opposite angles of the quadrilateral are supplementary.

    I'm not sure how to write this proof. Any help would be greatly appreciated!
    Sorry, I labelled the angles the same as your vertices.
    This was not intentional.

    Join all corners of the quadrilateral to the circle centre "o".
    you now have 4 isosceles triangles with the angles at the circumference within each triangle equal.

    Therefore 2A+2B+2C+2D =360 degrees.
    A+B+C+D=180 degrees.

    (A+B)+(C+D)=180 degrees.
    (A+C)+(B+D)=180 degrees.
    Attached Thumbnails Attached Thumbnails guadrilateral inscribed in a circle...-inscribed-quadrilateral.jpg  
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  3. #3
    mdk
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    Thank you

    Thank you so much for the help and the picture. It really helps to see it.
    mdk
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