The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center 
as the pivot point. It therefore has trilinear equation
It passes through Kimberling centers 
for 
(incenter 
), 3 (circumcenter 
), 4 (orthocenter 
), 5 (nine-point center 
),
17 (first Napoleon point), 18 (second
Napoleon point), 54 (Kosnita point), 61, 62,
195, 627, 628, 2120, 2121, as well as the excenters 
, 
, and 
.
See also
Pivotal Isogonal Cubic,
Triangle Cubic
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References
Čerin, Z. "On the Cubic of Napoleon." J. Geom. 66, 55-71, 1999.Gibert, B. "Napoleon-Feuerbach
Cubic." http://perso.wanadoo.fr/bernard.gibert/Exemples/k005.html.Referenced
on Wolfram|Alpha
Napoleon-Feuerbach Cubic
Cite this as:
Weisstein, Eric W. "Napoleon-Feuerbach Cubic."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Napoleon-FeuerbachCubic.html
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