The Euler line of a triangle is a line going through several important triangle centers, including the [u]orthocenter[/u], [u]circumcenter[/u], [u]centroid[/u], and [u]center of the nine point circle[/u]. The fact that such a line exists for all non-equilateral triangles is quite unexpected, made more impressive by the fact that the relative distances between the triangle centers remain constant.[br]Blue lines are altitudes, orange medians, green perpendicular bisectors, and the red line is the Euler line[br][br]In the diagram above, the points[br]- H represents the orthocenter,[br]- N represents the nine-point center,[br]- G represents the centroid,[br]- O represents the circumcenter.