The Centroid, Circumcenter, and Orthocenter Are Collinear

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For a triangle , let be the centroid (the point of intersection of the medians of a triangle), the circumcenter (the center of the circumscribed circle of ), and the orthocenter (the point of intersection of its altitudes). Then , , and are collinear and . Note that and can be located outside of the triangle.

Contributed by: Jaime Rangel-Mondragon (July 2011)
Open content licensed under CC BY-NC-SA


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