Rational Tangential Complete Quadrilateral

A complete quadrilateral is a figure with four infinite lines , , , with six points of intersection , , , and , , where each line goes through three of the six points. Including the points and , the four lines are , , and . The diagonals of this quadrilateral are thus , and .

A tangential complete quadrilateral has all lines tangent to a circle.

A rational version has a rational distance between any two of the six points on the same line. Also, the circle has rational radius.

If , , are rational numbers, then the edge lengths of a rational tangential complete quadrilateral can be written in the following form:

,

,

,

,

,

,

,

,

,

,

,

,

.