Euler straight line

The straight line passing through the point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its medians, and the centre $O$ 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

$$OH:SH=1:2$$

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

References

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