incircle

The incircle or inscribed circle of a triangle is a circle interior to the triangle and tangent to its three sides.

Moreover, the incircle of a polygon is an interior circle tangent to all of the polygon's sides. Not every polygon has an inscribed circle, but triangles always do.

The center of the incircle is called the incenter, and it's located at the point where the three angle bisectors intersect.

If the sides of a triangle are $x$ , $y$ and $z$ , the area $A$ and the semiperimeter $p$ , then the radius of incircle may be calculated from $$r = \frac{2A}{x+y+z} = \frac{A}{p} = \sqrt\frac{(p-x)(p-y)(p-z)}{p}.$$