The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters
 |
(1)
|
The triangle centroid 
and the symmedian point 
of the triangle are its foci, giving
as its center.
Its Brianchon point is Kimberling center 
,
which is the midpoint of the line 
(where 
is the symmedian point
and 
is the triangle centroid and has triangle
center function
 |
(2)
|
The triangle formed by the contact points of the Lemoine inellipse with the reference triangle is the Lemoine triangle.
The polar triangle of the Lemoine inellipse is the Lemoine triangle.
The semimajor axes lengths are
 |  |  |
(3)
|
 |  |  |
(4)
|
giving the area as
 |
(5)
|
where 
is the area of the reference triangle.
No Kimberling centers lie on the Lemoine inellipse.
