Definition:Excircle of Triangle

Excircle
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.

This is also sometimes refered to as an escribed circle.



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

Excenter
The center of an excircle is called an excenter.

Exradius
The radius of an excircle is called an exradius.

Note
There are three excircles for every triangle, unlike incircles and circumcircles.