Excircles

An excircle of a triangle is a circle that lies outside the triangle and is tangent to one side of the triangle and to the extensions of the other two sides. Every triangle has three excircles, each associated with one of its sides.

Important properties

• Each excircle touches one side of the triangle and the extensions of the other two sides.

• The center of an excircle is called an excenter. There are three excenters, each found as the intersection of the external angle bisectors of two angles and the internal angle bisector of the third angle.

• The radius of an excircle is called the exradius.

• The excircle is always outside the triangle.