The de Longchamps ellipse of a triangle is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt . (Since a conic is uniquely determined by five points, the conic is already specified with only five of these six points.)
The de Longchamps ellipse is centered at the incenter of the reference triangle, and has trilinear equation
which can also be written
It passes through the points , , and (Weisstein, Oct. 17 and Nov. 22, 2004).