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# First Fermat Point

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) (3)

and is Kimberling center (Kimberling 1998, p. 67).

It also arises in Napoleon's theorem.

Fermat Axis, Fermat Points, Napoleon's Theorem, Second Fermat Point

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## References

Kazarinoff, N. D. Geometric Inequalities. New York: Random House, pp. 117-118, 1961.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Fermat Point." http://faculty.evansville.edu/ck6/tcenters/class/fermat.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(13)=1st Isogonic Center." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X13.

## Referenced on Wolfram|Alpha

First Fermat Point

## Cite this as:

Weisstein, Eric W. "First Fermat Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FirstFermatPoint.html