# Orthocenter

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Related to Orthocenter: Circumcenter

## orthocenter

[¦ȯr·thō′sen·tər]
(mathematics)
The point at which the altitudes of a triangle intersect.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Orthocenter

the point of intersection of the three altitudes of a triangle. In any triangle the point of intersection of the medians, the center of a circumscribed circle, and the orthocenter all lie on one line.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
For this purpose, we look at the motion of the orthocenter. Specifically, we relate [P.sup.2] to the displacement of z along the line of its motion, which we denote as l.
They intersect at the point [H.sub.o] orthocenter of the tetrahedron (fig.
We also have proved that the orthogonal projection of the orthocenter of the Pavillet tetrahedron on the plane of its base triangle is the Gergonne point of its base triangle.
We generalized directly to 3D, and we defined the orthocenter as the point where the four altitudes of a tetrahedron intersect.
( This work is presented with Cabri3D, [3]) Then, we made a conjecture that the orthocenter exists when at least one facet is an equilateral triangle.
We proved that the four altitudes are concurrent on a point if at least one altitude intersects with the opposite plane's orthocenter. Also, we proved that the four altitudes intersect with their opposite facet's orthocenter if the orthocenter exists.
In addition, we've also shown that all orthotetrahedrons (=tetrahedrons with orthocenter) have circumcenter, centroid, and orthocenter to be collinear.
[2] Kim, Dohyun, Cabri3D File (Orthocenter_RightTetrahedron.cg3) containing the orthocenter of a right tetrahedron, 200;
[4] Kim, Dohyun, Cabri3D File (Orthocenter_CounterExample.cg3) containing the counterexample on conjectures for an orthocenter, 2007
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