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Math Help - Prove that trapezoid inscribed in a circle is isosceles.

  1. #1
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    Prove that trapezoid inscribed in a circle is isosceles.

    Prove that trapezoid inscribed in a circle is isosceles?
    I have a trapezoid ABCD ...dont know how to prove digonals AC = BD? Help...
    Last edited by mr fantastic; June 4th 2010 at 08:04 AM. Reason: Re-titled.
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  2. #2
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    Quote Originally Posted by winsome View Post
    Prove that trapezoid inscribed in a circle is isosceles?
    I have a trapezoid ABCD ...dont know how to prove digonals AC = BD? Help...
    Draw lines from the center of thecircle to each vertex. consider the triangles formed and use the fact that the sides from the center to the vertices are all congruent. You will probably need to consider two cases: where the center of the circle is inside the trapezoid and where it isn't.
    Last edited by HallsofIvy; December 28th 2009 at 04:24 AM.
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  3. #3
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    Hello, winsome!

    Is it really this simple?


    Prove that trapezoid inscribed in a circle is isosceles.
    Code:
                  * * *
            A o-----------o B
            */             \*
           */               \*
           /                 \
        D o-------------------o C
          *                   *
          *                   *
    
           *                 *
            *               *
              *           *
                  * * *

    \begin{array}{cccc}AB \parallel CD && \text{D{e}finition of trapezoid} \\ \\<br />
\text{arc}(AD) \,=\,\text{arc}(BC) && \text{Parallel lines intercept equal arcs} \\ \\<br />
AD \:=\:BC &&\text{Equal arcs subtend equal chords.} \\ \\<br />
\therefore \:ABCD\text{ is isosceles.} \end{array}

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, winsome!

    Is it really this simple?


    Code:
                  * * *
            A o-----------o B
            */             \*
           */               \*
           /                 \
        D o-------------------o C
          *                   *
          *                   *
    
           *                 *
            *               *
              *           *
                  * * *

    \begin{array}{cccc}AB \parallel CD && \text{D{e}finition of trapezoid} \\ \\<br />
\text{arc}(AD) \,=\,\text{arc}(BC) && \text{Parallel lines intercept equal arcs} \\ \\<br />
AD \:=\:BC &&\text{Equal arcs subtend equal chords.} \\ \\<br />
\therefore \:ABCD\text{ is isosceles.} \end{array}



    Thanx for Reply but i have few more issues,
    is there another solution if we not consider
    the property of Parallel lines intercept equal arcs ?as i need the solution without using this property.
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