The incenterMathworldPlanetmath of a geometrical shape is the center of the incircleMathworldPlanetmath (if it has any). The radius of the incircle is sometimes called the inradius.

On a triangleMathworldPlanetmath the incenter always exists and it is the intersectionMathworldPlanetmath point of the three internal angle bisectors. So in the next picture, AX,BY,CZ are angle bisectorsMathworldPlanetmath, and AB,BC,CA are tangent to the circle.

Title incenter
Canonical name Incenter
Date of creation 2013-03-22 12:11:12
Last modified on 2013-03-22 12:11:12
Owner mps (409)
Last modified by mps (409)
Numerical id 11
Author mps (409)
Entry type Definition
Classification msc 51M99
Synonym incentre
Related topic Incircle
Related topic LengthsOfAngleBisectors
Related topic AngleBisectorAsLocus
Related topic OrthocenterMathworldPlanetmath
Related topic Triangle
Related topic CevasTheorem
Related topic LemoinePoint
Related topic GergonnePoint
Related topic GergonneTriangle
Related topic TrigonometricVersionOfCevasTheorem
Defines inradius