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 At 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.
 

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.
 

 
 
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