Geometry
Triangle centers
Centroid, circumcenter, incenter, orthocenter — four points every triangle hides.
Every triangle has not one but four special centers — each made by intersecting a different family of lines. They show up in surveying, architecture and even computer graphics.
The big four
- Centroid — where the three medians meet. The triangle's balance point. Always inside.
- Circumcenter — where perpendicular bisectors of the sides meet. Center of the circumscribed circle.
- Incenter — where the three angle bisectors meet. Center of the largest inscribed circle.
- Orthocenter — where the three altitudes meet. Can be inside, on, or outside the triangle.
Euler line — for any non-equilateral triangle, the centroid, circumcenter and orthocenter all lie on the same straight line. The centroid sits exactly one-third of the way from the orthocenter to the circumcenter.