Difference between revisions of "Euler line"
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Let <math>ABC</math> be a triangle
Let <math>ABC</math> be a triangle<math>H</math>, [[nine-point center]] , [[centroid]] , [[circumcenter]] [[De Longchamps point]] these points are [[collinear]] the line passes through points <math>H, N, G, O, L</math> is called Euler lineis named after [[Leonhard Euler]].
distances between these points:
* <math>OG:GN:NH :1:3</math>
[[orthic triangle]]<math>\triangle H_AH_BH_C</math>, Euler lines of <math>\triangle AH_BH_C</math>,<math>\triangle BH_CH_A</math>, <math>\triangle CH_AH_B</math> concurat <math></math>nine-point center .
Revision as of 14:53, 5 November 2006
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Let be a triangle with orthocenter , nine-point center , centroid , circumcenter and De Longchamps point . Then these points are collinear and the line passes through points is called the Euler line of . It is named after Leonhard Euler.
Certain fixed ratios hold among the distances between these points: