Harmonic quadrilateral

In Euclidean geometry, a harmonic quadrilateral is a quadrilateral whose four vertices lie on a circle, and whose pairs of opposite edges have equal products of lengths.

Harmonic quadrilaterals have also been called harmonic quadrangles. They are the images of squares under Möbius transformations. Every triangle can be extended to a harmonic quadrilateral by adding another vertex, in three ways. The notion of Brocard points of triangles can be generalized to these quadrilaterals.