# circumcenter

## Derivation of Formula for Radius of Circumcircle

The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by

$R = \dfrac{abc}{4A_t}$

where A_{t} is the area of the inscribed triangle.

## 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.