# incenter

## Derivation of Formula for Radius of Incircle

The radius of incircle is given by the formula

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

where A_{t} = area of the triangle and s = semi-perimeter.

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## 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.

The radius of incircle is given by the formula

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

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

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