Euler line

In any triangle, the orthocenterMathworldPlanetmath H, the centroid G and the circumcenterMathworldPlanetmath O are collinearMathworldPlanetmath, and OG/GH=1/2. The line passing by these points is known as the Euler lineMathworldPlanetmath of the triangle.

This line also passes by the center of the nine-point circleMathworldPlanetmath (or Feuerbach circle) N, and N is the midpointMathworldPlanetmathPlanetmathPlanetmath of OH.

Title Euler line
Canonical name EulerLine
Date of creation 2013-03-22 11:44:25
Last modified on 2013-03-22 11:44:25
Owner drini (3)
Last modified by drini (3)
Numerical id 18
Author drini (3)
Entry type Theorem
Classification msc 51-00
Classification msc 58A05
Classification msc 83E15
Classification msc 83D05
Classification msc 83E05
Classification msc 83E50
Classification msc 81-00
Classification msc 83-00
Classification msc 82-00
Related topic Triangle
Related topic Orthocenter
Related topic Centroid
Related topic Collinear
Related topic Midpoint
Related topic OrthicTriangle
Related topic CenterOfATriangle
Related topic EulerLineProof