Construction: Excenters

Let's say you desperately need to go the the bathroom but your Math teacher is holding you back until you draw her the excenters of a given triangle $ABC$ .

But you manage to amaze your Math teacher after doing the following :

1. Extend the sides of the triangle beyond $A,B$ and $C$.

2. Using a compass, you skilfully draw tha angle bisectors of the exterior angles of triangle $ABC$. That is, the supplementary angle of $\angle A, \angle B$ and $\angle C$.

3. Then you join the lines you just drew and get a big triangle.

[image from http://upload.wikimedia.org/wikipedia/commons/3/36/Excenter_triangle.png)

1. You tell your teacher " The vertices of this new triangle are the excenters" with a big grin on your face.

So she let you go. But it turns out you felt like you didn't need the bathroom anymore. Oh well :)