# Euler straight line

From Encyclopedia of Mathematics

The straight line passing through the point of intersection of the altitudes of a triangle, the point of intersection of its medians, and the centre of the circle circumscribed to it. If the Euler line passes through a vertex of the triangle, then the triangle is either isosceles or right-angled, or both right-angled and isosceles. The segments of the Euler line satisfy the relation

This line was first considered by L. Euler (1765).

#### Comments

#### References

[a1] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963) |

**How to Cite This Entry:**

Euler straight line.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Euler_straight_line&oldid=16830

This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article