The term "Lemoine triangle," introduced in this work, denotes the Cevian triangle 
of Kimberling center 
.
It is the polar triangle of the Lemoine inellipse.
It has the trilinear vertex matrix
![[0 (ac)/(-2a^2+b^2-2c^2) (ab)/(-2a^2-2b^2+c^2); (bc)/(a^2-2b^2-2c^2) 0 (ab)/(-2a^2-2b^2+c^2); (bc)/(a^2-2b^2-2c^2) (ac)/(-2a^2+b^2-2c^2) 0].](/images/equations/LemoineTriangle/NumberedEquation1.svg) |
The vertices are the points of contact of the Lemoine inellipse with the sidelines of the reference triangle.
