An excenter of a triangle is a point at which the line bisecting one interior angle meets the bisectors of the two exterior angles on the opposite side. This is the center of a circle, called an excircle which is tangent to one side of the triangle and the extensions of the other two sides. Every triangle has three excenters and three excircles. The radius of excircle is called the exradius.

In the following applet , the internal bisector of angle B of triangle ABC and bisectors of exterior angles at A and C meet at E

In the following applet , the internal bisector of angle B of triangle ABC and bisectors of exterior angles at A and C meet at E

_{1}. E_{1}is one of the excenters of triangle ABC.