The first Fermat point 
(or 
) (sometimes simply called "the Fermat point,"
Torricelli point, or first isogonic center) is the point 
which minimizes the sum of distances from 
, 
, and 
in an acute triangle,
 |
(1)
|
It has equivalent triangle center functions
 |  |  |
(2)
|
 |  | ![bc[c^2a^2+(c^2+a^2-b^2)^2][a^2b^2-(a^2+b^2-c^2)^2][4Delta-sqrt(3)(b^2+c^2-a^2)]](/images/equations/FirstFermatPoint/Inline12.svg) |
(3)
|
and is Kimberling center 
(Kimberling 1998, p. 67).
It also arises in Napoleon's theorem.
