Construct a triangle $ABC$ given that $AB = 5 \; cm$, $BC = 6 \; cm$ and $\angle ABC = 120^\circ$. Construct the incircle of the triangle. Measure and record the radius of the incircle.
$\triangle ABC$ is constructed with $AB = 5 \; cm$, $BC = 6 \; cm$ and $\angle ABC = 120^\circ$ (blue and orange construction arcs).
The angle bisectors of $\angle A$ and $\angle C$ are drawn. The two angle bisectors intersect at point $I$ (violet construction arcs and lines).
From the point $I$ draw $IP$ perpendicular to side $AC$ of the triangle (red construction arcs and lines).
With $I$ as center and $IP$ as radius, draw a circle which will touch all the sides of the triangle drawn.
This circle is required inscribing circle of $\triangle ABC$.
Inradius $= IP = 1.2 \; cm$ (by measurement).