The "middle" of a triangle, Method #3: The incenter

We come to another idea of where the center of a triangle is, a method called the incenter.  This is the point that is the center of the circle that is inscribed within the triangle, tangent to all three sides.

Once again, the point is defined as the meeting place for three lines. This time, the lines are the angle bisectors for the three angles. Like the centroid, the incenter must be in the interior of the triangle, which is not true for the circumcenter of an obtuse triangle.