Euler straight line

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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).



[a1] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
How to Cite This Entry:
Euler straight line. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article