# 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**.

### Exradius

A radius of an excircle of a triangle is called an **exradius of the triangle**.

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

## Also known as

An **excircle** is also sometimes referred to as an **escribed circle**.