The angle bisectors of the angles of a triangle are concurrent (they intersect in one common point). The point of concurrency of the angle bisectors is called the **incenter **of the triangle. The point of concurrency is always located in the interior of the triangle.

NOTE: The point of concurrency of the angle bisectors of a triangle (the incenter) is the center of an inscribed circle within the triangle. |

An

inscribed circle is a circle positioned within a figure such that the circle is

** tangent **to each of the sides of the figure. In this case, the circle is tangent to the sides of the triangle. A circle is tangent to a segment (or line) if it touches the segment only once, but does not cross the segment. Since radii in a circle are of equal length, the

incenter is equidistant from the sides of the triangle.