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# Lemoine Inellipse

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.

## See also

Brianchon Point, Inconic, Inellipse, Lemoine Triangle

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## Cite this as:

Weisstein, Eric W. "Lemoine Inellipse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemoineInellipse.html