Engineering Mathematics

incenter

Derivation of Formula for Radius of Incircle

The radius of incircle is given by the formula
 

$r = \dfrac{A_t}{s}$

 

where At = area of the triangle and s = semi-perimeter.
 

Centers of a Triangle

This page will define the following: incenter, circumcenter, orthocenter, centroid, and Euler line.
 

Incenter
Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle.
 

incenter-incircle.jpg

 

The radius of incircle is given by the formula

$r = \dfrac{A_t}{s}$

where At = area of the triangle and s = ½ (a + b + c). See the derivation of formula for radius of incircle.