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Math Help - Diagonals of Cyclic Quad

  1. #1
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    Diagonals of Cyclic Quad

    Prove that if the diagonals of a cyclic quadrilateral are equal then so is a pair of opposite sides.
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  2. #2
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    Hello, cedricc!

    Prove that if the diagonals of a cyclic quadrilateral are equal ,
    then so is a pair of opposite sides.
    Code:
                  * * *
              *           *
          A o---------------o B
           *  *            *|*
                *         * |
          *       *      *  | *
          *         *   *   | *
          *           **    | *
                      * *   |
           *         *    * |*
            *       *       o C
              *    *      *
                  o * * 
                  D

    Draw AD and CD.
    We have cyclic quadrilateral ABCD.


    \begin{array}{ccccc}1. & \overline{AC} \:=\: \overline{BD} & & 1. & \text{Given} \\ \\<br /> <br />
2. & \text{arc}(ADC) \:=\: \text{arc}(BCD) & & 2. & \text{Equal chords =  equal arcs} \\ \\<br /> <br />
3. & \text{arc}(CD) \:=\:\text{arc}(CD) && 3. & \text{Identity axiom} \\ \\<br /> <br />
4. & \text{arc}(AD) \:=\:\text{arc}(BC) && 4. & \text{Subtraction postulate} \end{array}

    \begin{array}{ccccc}5. & \qquad \quad\overline{AD} \:=\:\overline{BC} && \qquad\quad 5. & \text{Equal arcs = equal chords.}<br />
\end{array}

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