# Orthocentre

From Encyclopedia of Mathematics

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*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:**

Orthocentric triangle.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Orthocentric_triangle&oldid=42286