Difference between revisions of "Orthocentre"
From Encyclopedia of Mathematics
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| − | The point of intersection of the three altitudes of a triangle. The orthocentre of a triangle lies on the [[Euler | + | The point of intersection of the three altitudes of a triangle, one of the classical [[triangle centre]]s. The orthocentre of a triangle lies on the [[Euler line]]. The mid-points of the three sides, the mid-points of the segments joining the orthocentre to the three vertices and the feet of the altitudes of the triangle lie on one circle. The orthocentre is the centre of the circle inscribed in the orthocentric triangle, i.e. the triangle whose vertices are the feet of the altitudes of the given one. |
====Comments==== | ====Comments==== | ||
| − | The inscribed circle mentioned above is the so-called [[ | + | The inscribed circle mentioned above is the so-called [[nine-point circle]]. |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''1–2''' , Springer (1987) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | ||
Latest revision as of 19:18, 6 November 2016
of a triangle
The point of intersection of the three altitudes of a triangle, one of the classical triangle centres. The orthocentre of a triangle lies on the Euler line. The mid-points of the three sides, the mid-points of the segments joining the orthocentre to the three vertices and the feet of the altitudes of the triangle lie on one circle. The orthocentre is the centre of the circle inscribed in the orthocentric triangle, i.e. the triangle whose vertices are the feet of the altitudes of the given one.
Comments
The inscribed circle mentioned above is the so-called nine-point circle.
References
| [a1] | M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French) |
| [a2] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963) |
How to Cite This Entry:
Orthocentre. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Orthocentre&oldid=13282
Orthocentre. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Orthocentre&oldid=13282
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article