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.

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Re: Isosceles Trapezoid Proof

Draw a perpendicular bisector of the sides and mark their point of intersection as . Now is equidistant from and . With as the center and radius ( ) draw a circle this circle passes through and . This will also pass through . As quadrilateral ABCD is cyclic.

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(Refer to the figure attached).

Kalyan.