Which point of concurrency is formed by the angle bisectors of a triangle?

The point of concurrency that is formed by the intersection of the angle bisectors of a triangle is known as the incenter. The incenter has a significant property: it is equidistant from all three sides of the triangle, which means that it is the center of the circle inscribed within the triangle, called the incircle. This characteristic arises because the angle bisectors divide the angles of the triangle into two equal parts, leading to a unique point where they all meet and from which a circle can be drawn to touch all three sides of the triangle.

In contrast, the centroid is the point where the three medians intersect, the circumcenter is where the perpendicular bisectors of the sides meet, and the orthocenter is the point where the altitudes of the triangle intersect. Each of these points of concurrency has different geometric properties and serves different functions in relation to the triangle. The incenter is specifically related to the triangle's angles and the distances to its sides, which is what confirms its unique role among the points of concurrency.