What feature is unique to an incenter of a triangle?

The incenter of a triangle is indeed the center of the circle inscribed within the triangle, which is a key characteristic that sets it apart from other triangle centers. This circle is known as the incircle, and it touches each side of the triangle at exactly one point, thus demonstrating the incenter’s role in relation to the triangle's geometry.

Additionally, the incenter is determined by the intersection of the angle bisectors of the triangle. Each angle bisector divides the angle into two equal parts and their intersection point is equidistant from all three sides of the triangle, which is the defining property that allows for the construction of the incircle.

This unique position of the incenter, being inside the triangle and serving as the origin of the incircle, plays a vital role in various geometric applications and proofs. The other features, such as centroid and locations of medians, refer to different triangle centers entirely and are characterized by different properties and functions within triangle geometry.