Content Knowledge
The Euler line of a triangle is a line going through several important triangle centers, including the orthocenter, circumcenter, centroid, and center of the nine point circle. 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.
Blue lines are altitudes, orange medians, green perpendicular bisectors, and the red line is the Euler line
In the diagram above, the points
- H represents the orthocenter,
- N represents the nine-point center,
- G represents the centroid,
- O represents the circumcenter.