# Definition:Excircle of Triangle

## Definition

Given a triangle, extend two sides in the direction opposite their common vertex.

The circle tangent to both of these lines and to the third side of the triangle is called an excircle.

There are three excircles for every triangle.

### Excenter

The center of an excircle of a triangle is called an excenter of the triangle.

In the above diagram, $r$ is an exradius.