View source for Orthocentre

''of a triangle''

The point of intersection of the three altitudes of a triangle. The orthocentre of a triangle lies on the [[Euler straight line|Euler straight 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|nine-point circle]].

====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>