Incircle of a Triangle Geometry construction using a compass and straightedge As can be seen in Incenter of a Triangle, the three angle bisectors of any triangle always pass through its incenter. In this construction, we only use two, as this is sufficient to define the point where they intersect. We bisect the two angles using the method described in Bisecting an Angle. The point where the bisectors cross is the incenter. We then draw a circle that just touches the triangles's sides.