Euler's line
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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.
Other notable points that lie on this line are the de Longchamps point, the Schiffler point, the Exeter point and the far-out point. (these points are not shown).
The Euler line is its own complement, and therefore also its own anticomplement.
[edit] External links
- Altitudes and the Euler Line at cut-the-knot
- Euler Line and 9-Point Circle at cut-the-knot
- Euler Line, Nine-Point Circle, and Nine-Point Center Interactive illustration with 22 steps at Geometry from the Land of the Incas.
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