The intersection of the three Altitudes of a Triangle
is called the orthocenter. Its Trilinear Coordinates are

(1) |

(2) |

The Circumcenter and orthocenter are Isogonal Conjugate points.
The orthocenter lies on the Euler Line.

(3) |

(4) |

(5) |

Any Hyperbola circumscribed on a Triangle and passing through the orthocenter is Rectangular, and has its center on the Nine-Point Circle (Falisse 1920, Vandeghen 1965).

**References**

Altshiller-Court, N. *College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed.*
New York: Barnes and Noble, pp. 165-172, 1952.

Carr, G. S. *Formulas and Theorems in Pure Mathematics, 2nd ed.* New York: Chelsea, p. 622, 1970.

Coxeter, H. S. M. and Greitzer, S. L. *Geometry Revisited.* Washington, DC: Math. Assoc. Amer., pp. 36-40, 1967.

Dixon, R. *Mathographics.* New York: Dover, p. 57, 1991.

Falisse, V. *Cours de géométrie analytique plane.* Brussels, Belgium: Office de Publicité, 1920.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, pp. 165-172 and 191, 1929.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' *Math. Mag.* **67**, 163-187, 1994.

Kimberling, C. ``Orthocenter.'' http://cedar.evansville.edu/~ck6/tcenters/class/orthocn.html.

Vandeghen, A. ``Some Remarks on the Isogonal and Cevian Transforms. Alignments of Remarkable Points of a Triangle.''
*Amer. Math. Monthly* **72**, 1091-1094, 1965.

© 1996-9

1999-05-26