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

$$r=\frac{2A}{x+y+z}=\frac{A}{p}=\sqrt{\frac{(p-x)(p-y)(p-z)}{p}}.$$

Title	incircle
Canonical name	Incircle
Date of creation	2013-03-22 12:11:09
Last modified on	2013-03-22 12:11:09
Owner	drini (3)
Last modified by	drini (3)
Numerical id	8
Author	drini (3)
Entry type	Definition
Classification	msc 51M99
Related topic	LemoinePoint
Related topic	Incenter
Related topic	LemoineCircle
Related topic	Triangle
Related topic	GergonnePoint
Related topic	GergonneTriangle
Related topic	ConstructionOfTangent