# The Centroid, Circumcenter, and Orthocenter Are Collinear

The Centroid, Circumcenter, and Orthocenter Are Collinear

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.

T

M

O

T

H

M

O

H

HM=2MO

H

O