The incentral triangle Δ I_A I_B I_C is the Cevian triangle of a triangle Δ A B C with respect to its incenter I. It is therefore also the triangle whose vertices are determined by the intersections of the reference triangle's angle bisectors with the respective opposite sides. Its trilinear vertex matrix is [0 | 1 | 1 1 | 0 | 1 1 | 1 | 0]. It is perspective to every anticevian triangle. It is the cyclocevian triangle with respect to Kimberling center X_1029.

angle bisector | Cevian triangle | excentral triangle | incenter | incentral circle | incircle | symmedian point