The Lemoine inellipse 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 
,
the midpoint of 
, as its center.
Its Brianchon point is Kimberling center 
,
which 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 axis and semiminor axis 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.
