\begin{definition}[Definition:Pythagorean Quadrilateral]
A '''Pythagorean quadrilateral''' is a convex quadrilateral whose diagonals intersect at right angles, and is formed by fitting four right triangles with integer-valued sides.
The interest is finding solutions where no two triangles are similar.
The smallest Pythagorean quadrilateral is formed by the triangles with side lengths:
:$\tuple {25, 60, 65}, \tuple {91, 60, 109}, \tuple {91, 312, 325}, \tuple {25, 312, 313}$
The smallest primitive Pythagorean quadrilateral, where each Pythagorean triple is primitive is:
:$\tuple {28435, 20292, 34933}, \tuple {284795, 20292, 285517}, \tuple {284795, 181908, 337933}, \tuple {28435, 181908, 184117}$
The smallest anti-primitive Pythagorean quadrilateral, where no Pythagorean triples are primitive is:
:$\tuple {1209, 6188, 6305}, \tuple {10659, 6188, 12325}, \tuple {10659, 23560, 25859}, \tuple {1209, 23560, 23591}$
with common divisors:
:$13, 17, 19, 31$
\end{definition}