The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as the inradius. The incenter can be constructed as the intersection of angle bisectors. It is also the interior point for which distances to the sides of the triangle are equal. It has trilinear coordinates 1:1:1, i.e., triangle center function α_1 = 1, and homogeneous barycentric coordinates (a, b, c). It is Kimberling center X_1.

circumcenter | cyclic quadrilateral | excenter | Gergonne point | incentral triangle | incircle | inradius | Nagel line | orthocenter | orthocentric centroid