# Isosceles Trapezoid Proof

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• September 4th 2012, 09:35 AM
Senators88
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.
• September 6th 2012, 08:45 AM
kalyanram
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Re: Isosceles Trapezoid Proof
Draw a perpendicular bisector of the sides $AD$ and $DC$ mark their point of intersection as $O$. Now $O$ is equidistant from $A,D$ and $C$. With $O$ as the center and radius $OA$ ( $=OD= OC$) draw a circle this circle passes through $A,D$ and $C$. This will also pass through $B$. As quadrilateral ABCD is cyclic.
$Q.E.D$.

(Refer to the figure attached).

Kalyan.
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