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Thread: Isosceles Trapezoid Proof

  1. #1
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    Isosceles Trapezoid Proof

    An isosceles trapezoid has points A,B,C, and D where AD and BC are parallel. Prove that any isosceles trapezoid can be inscribed in a circle. Do this by finding a unique point 0 which is equidistant from points A,B,C, and D. Write a proof on how to construct this circle.

    Note: Sides AB, BC, and CD have length 1 and side AD has length square root of 3.
    Last edited by Senators88; Sep 4th 2012 at 10:46 AM.
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  2. #2
    Member kalyanram's Avatar
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    Re: Isosceles Trapezoid Proof

    Draw a perpendicular bisector of the sides $\displaystyle AD$ and $\displaystyle DC$ mark their point of intersection as $\displaystyle O$. Now $\displaystyle O$ is equidistant from $\displaystyle A,D$ and $\displaystyle C$. With $\displaystyle O$ as the center and radius $\displaystyle OA$ ($\displaystyle =OD= OC $) draw a circle this circle passes through $\displaystyle A,D$ and $\displaystyle C$. This will also pass through $\displaystyle B$. As quadrilateral ABCD is cyclic.
    $\displaystyle Q.E.D$.

    (Refer to the figure attached).

    Kalyan.
    Attached Thumbnails Attached Thumbnails Isosceles Trapezoid Proof-isotra.png  
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