Incircle and Excircles of A Triangle - Coordinates of The Incenter

Coordinates of The Incenter

The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices using the side lengths of the triangle as weights. (The weights are positive so the incenter lies inside the triangle as stated above.) If the three vertices are located at, and, and the sides opposite these vertices have corresponding lengths, and, then the incenter is at

where

Trilinear coordinates for the incenter are given by

Barycentric coordinates for the incenter are given by