Geometry construction using a compass and straightedge
As can be seen in
Incenter of a Triangle,
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
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.