What point in a triangle is the intersection of the angle bisectors?

The incenter of a triangle is the point where the angle bisectors of all three angles intersect. This means it is equally distant from all three sides of the triangle, which is a key characteristic of the incenter. The incenter is also the center of the incircle, which is the largest circle that fits inside the triangle, tangent to all three sides.

During the construction of a triangle's incenter, the angle bisectors are drawn from each vertex to the opposite side, creating segments that split each angle into two equal parts. The point where these segments meet is exactly where the incenter lies.

In contrast, the other points mentioned have different roles in triangle geometry. The orthocenter is the intersection of the altitudes; the circumcenter is where the perpendicular bisectors of the sides intersect, serving as the center of the circumcircle; and the centroid is the point where the medians of the triangle intersect. While each of these points is significant in different contexts, they do not share the property of being the intersection of angle bisectors. This clearly establishes why the incenter is the correct answer in this question.