A Rational Bicentric Quadrilateral with a Rational Area
A bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.[more]
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
 Wikipedia. "Bicentric Quadrilateral." (Apr 7, 2023) en.wikipedia.org/wiki/Bicentric_quadrilateral.