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
Some (usually older) sources hyphenate: ex-circle.

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