The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Excircle of a Triangle

The excircle is the circle whose center is defined by the intersection of the external angle bisectors of two vertices A and B (angles α' and β'), and which is tangent to the side c between the two vertices. The excircle is also tangent to the extension of the sides a and b.

Each triangle has three excircles, whose radii are determined by the following equations:

Note that the excircles are not necessarily tangent to the incircle.

Last Update: 2011-01-11