In geometry, Euler's line (red line in the image), named after Leonhard Euler, is the line passing through the orthocenter (blue), the circumcenter (green), the centroid (yellow), and the center of the nine-point circle (red point) of any triangle.

Leonhard Euler showed that in any triangle, those four points are collinear. The center of the nine-point circle lies midway between the orthocenter and the circumcenter, and the distance from the centroid to the circumcenter is half that from the centroid to the orthocenter.

External links

• Altitudes and the Euler Line at cut-the-knot
• Euler Line and 9-Point Circle at cut-the-knot

Triangles

Eulersche Gerade | Recta de Euler | Droite d'Euler | Euler-egyenes | オイラー線 | Prosta Eulera | Прямая Эйлера | 歐拉線