Notable points and lines in a triangle

A triangle has several notable points, each defined by the intersection of certain lines associated with the triangle. The most common are:

• The centroid: intersection of medians
• The incenter: intersection of angle bisectors
• The circumcenter: intersection of perpendicular bisectors
• The orthocenter: intersection of altitudes Each of these points has unique properties and geometric significance.

Important properties

• The centroid divides each median in a 2:1 ratio.

• The incenter is the center of the inscribed circle (incircle).

• The circumcenter is the center of the circumscribed circle (circumcircle).

• The orthocenter may lie inside, outside, or on the triangle depending on its type.

• Some notable points are always collinear (e.g., centroid, circumcenter, and orthocenter lie on the Euler line).