Definition:Excircle of Triangle

Definition
Let $\triangle ABC$ be a triangle whose sides are $a$, $b$ and $c$ opposite vertices $A$, $B$ and $C$ respectively.

Let sides $b$ and $c$ be produced beyond the vertices $C$ and $B$ respectively.

Let a circle be constructed tangent to both of these extensions to $b$ and $c$ lines and also to $a$.

The circle so constructed is called the excircle of $\triangle ABC$ $a$.


 * Excircle-of-Triangle.png

There are three excircles for every triangle.

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

The word ecircle can also be seen, mainly in the U.S.

Also see

 * Definition:Incircle of Triangle
 * Definition:Circumcircle of Triangle