Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers
of opposite squares. Then van Aubel's theorem states that
the two lines are of equal length and cross at a right
angle.
van Aubel's theorem is related to Napoleon's theorem and is a special case of the Petr-Neumann-Douglas
theorem. It is sometimes (incorrectly) known simply as Aubel's theorem (Casey
1888; Wells 1991, p. 11; Kimberling 2003, p. 23).
A second theorem sometimes known as van Aubel's theorem states that if is the Cevian
triangle of a point , then