orthocenter
The orthocenter of a triangle
is the point of intersection
of its three heights.
In the figure, is the orthocenter of .
The orthocenter lies inside, on a vertex or outside the triangle depending on the triangle being acute, right or obtuse respectively. Orthocenter is one of the most important triangle centers and it is very related with the orthic triangle
(formed by the three height’s foots). It lies on the Euler line
and the four quadrilaterals
are cyclic.
In fact,
- •
is the orthocenter of ;
- •
is the orthocenter of ;
- •
is the orthocenter of .
The four points , and form what is calledan orthocentric tetrad.
Title | orthocenter |
Canonical name | Orthocenter |
Date of creation | 2013-03-22 11:55:41 |
Last modified on | 2013-03-22 11:55:41 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 11 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 51-00 |
Related topic | HeightOfATriangle |
Related topic | Median |
Related topic | Triangle |
Related topic | EulerLine |
Related topic | OrthicTriangle |
Related topic | CEvasTheorem |
Related topic | CevasTheorem |
Related topic | CenterOfATriangle |
Related topic | Incenter![]() |
Related topic | TrigonometricVersionOfCevasTheorem |
Related topic | Centroid |
Defines | orthocentric tetrad |