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).
