Question

The angle bisector of a triangle are 32 &765​

Answer 1

The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal parts.

The angle bisectors meet at the incenter I, which has trilinear coordinates 1:1:1.

AngleBisectorsTriangle

The length t_1 of the bisector A_1T_1 of angle A_1 in the above triangle DeltaA_1A_2A_3 is given by

t_1^2=a_2a_3[1-(a_1^2)/((a_2+a_3)^2)],

where t_i=A_iT_i^_ and a_i=A_jA_k^_.

The points T_1, T_2, and T_3 have trilinear coordinates (0,1,1), (1,0,1), and (1,1,0), respectively, and form the vertices of the incentral triangle.