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A Rational Bicentric Quadrilateral with a Rational Area

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A bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.

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Suppose , , are rational numbers such that .

Let be the quadrilateral with edge lengths given by

,

,

,

.

Then is a bicentric quadrilateral with rational edge lengths and rational area

.

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Contributed by: Minh Trinh Xuan (June 14)
Open content licensed under CC BY-NC-SA

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Reference

[1] Wikipedia. "Bicentric Quadrilateral." (Apr 7, 2023) en.wikipedia.org/wiki/Bicentric_quadrilateral.

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