Definition of the Incenter of a Triangle : The incenter is one of the
triangle's points of concurrency formed by the intersection of the
triangle's 3 angle bisectors.
These three angle bisectors are always
concurrent and
always meet in the triangle's interior (unlike the
orthocenter which may or may not intersect in the interior). The incenter is the center of the
incircle . The incenter is the one point in the triangle whose distances to the sides are equal. (See picture)
If the
triangle is obtuse, such as the one on pictured below on the left, then the incenter is located in the triangle's interior.
If the
triangle is acute, then the incenter is also located in the triangle's interior.