Also known as the first Isogonic Center and the Torricelli Point. In a given
Acute Triangle , the Fermat point is the point which minimizes the sum of distances from , ,
and ,

(1) |

If all Angles of the Triangle are less than 120° (), then the Fermat point is the
interior point from which each side subtends an Angle of 120°, i.e.,

(2) |

(3) | |||

(4) |

The Antipedal Triangle is Equilateral and has Area

(5) |

Given three Positive Real Numbers , the ``generalized'' Fermat point is the point of a
given Acute Triangle such that

(6) |

**References**

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Gallatly, W. *The Modern Geometry of the Triangle, 2nd ed.* London: Hodgson, p. 107, 1913.

Greenberg, I. and Robertello, R. A. ``The Three Factory Problem.'' *Math. Mag.* **38**, 67-72, 1965.

Honsberger, R. *Mathematical Gems I.* Washington, DC: Math. Assoc. Amer., pp. 24-34, 1973.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.*
Boston, MA: Houghton Mifflin, pp. 221-222, 1929.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' *Math. Mag.* **67**, p. 174, 1994.

Kimberling, C. ``Fermat Point.'' http://cedar.evansville.edu/~ck6/tcenters/class/fermat.html.

Mowaffaq, H. ``An Advanced Calculus Approach to Finding the Fermat Point.'' *Math. Mag.* **67**, 29-34, 1994.

Pottage, J. *Geometrical Investigations.* Reading, MA: Addison-Wesley, 1983.

Spain, P. G. ``The Fermat Point of a Triangle.'' *Math. Mag.* **69**, 131-133, 1996.

Tong, J. and Chua, Y. S. ``The Generalized Fermat's Point.'' *Math. Mag.* **68**, 214-215, 1995.

van de Lindt, W. J. ``A Geometrical Solution of the Three Factory Problem.'' *Math. Mag.* **39**, 162-165, 1966.

© 1996-9

1999-05-26