Tangential polygon

All triangles are tangential, as are all regular polygons with any number of sides.

A convex polygon has an incircle if and only if all of its internal angle bisectors are concurrent.

[1] There exists a tangential polygon of n sequential sides a1, ..., an if and only if the system of equations has a solution (x1, ..., xn) in positive reals.

[2] If such a solution exists, then x1, ..., xn are the tangent lengths of the polygon (the lengths from the vertices to the points where the incircle is tangent to the sides).

389  For example, in the quadrilateral case where all sides are equal we can have a rhombus with any value of the acute angles, and all rhombi are tangential to an incircle.