If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a set of four points, no three collinear, and the six lines which join them. Note that a complete quadrilateral is different from a complete quadrangle. The midpoints of the sides of any complete quadrangle and the three diagonal points all lie on a conic known as the nine-point conic. If it is an orthocentric quadrilateral, the conic reduces to a circle.

complete quadrilateral | Ptolemy's theorem