The incenter of a triangle is the center of the triangle's incircle, which is the circle that is tangent to each side of the triangle. The incenter has several unique properties. Firstly, it is equidistant from each side of the triangle, meaning that the distance from the incenter to any side is the same. This distance is called the inradius of the triangle. Secondly, the incenter is the intersection point of the angle bisectors of the triangle. This means that the incenter divides the angle into two equal parts. Finally, the incenter is the center of symmetry for the incircle. This means that any line passing through the incenter and intersecting the incircle at two points will have those two points equidistant from the incenter. These properties make the incenter an important point in the study of triangles and their geometric properties.
