The radius of a polygon's incircle or of a polyhedron's insphere, denoted or sometimes (Johnson 1929). A polygon possessing an incircle is same
to be inscriptable or tangential.

The inradius of a regular polygon with sides and side length is given by

(1)

The following table summarizes the inradii from some nonregular inscriptable polygons.

where is the area
of the triangle, , ,
and are the side lengths, is the semiperimeter, is the circumradius,
and , , and
are the angles opposite sides , ,
and (Johnson 1929, p. 189). If two triangle
side lengths
and are known, together with the inradius
, then the length of the third side can be found by solving (1) for , resulting in a cubic
equation.

Equation (◇) can be derived easily using trilinear coordinates. Since the incenter is equally spaced
from all three sides, its trilinear coordinates are 1:1:1, and its exact trilinear
coordinates are .
The ratio
of the exact trilinears to the homogeneous coordinates is given by