The de Longchamps point 
is the reflection of the orthocenter 
about the circumcenter 
of a triangle.
It has triangle center function
 |
(1)
|
and is Kimberling center 
(Kimberling 1998, p. 70).
As a result of its definition, the de Longchamps point is collinear with the orthocenter 
and circumcenter 
of a triangle.
Distances to some other named triangle centers include
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
where 
is the triangle centroid, 
is the circumcenter, 
is the orthocenter,
is the Gergonne point, 
is the orthocenter, 
is the incenter, 
is the nine-point center,
and 
is the incenter.
The de Longchamps point is also the orthocenter of the anticomplementary triangle.
The Soddy line intersects the Euler line in the de Longchamps point (Oldknow 1996).
The de Longchamps point and Kimberling center 
(intersection 
of the Gergonne line
and orthic axis) form a diameter
of the GEOS circle.
