Van Aubel's theorem

In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral.

Van Aubel's theorem states that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another.

The theorem is named after Belgian mathematician Henricus Hubertus (Henri) Van Aubel (1830–1906), who published it in 1878.

[3] For complex (self-intersecting) quadrilaterals, the external and internal constructions for the squares are not definable.

In this case, the theorem holds true when the constructions are carried out in the more general way:[3] The segments joining the centers of the squares constructed externally (or internally) to the quadrilateral over two opposite sides have been referred to as Van Aubel segments.