In this section we will explore the incircle, excircle, and nine point circle of triangle ABC. First, look at the GSP construction of the incircle.

Now we will look at the constructions of the excircles for triangle ABC. The excircles, or the escribed circle, is a circle tangent to two nonadjacent lines coming off of the triangle ABC. The excircles lie on the external angle bisector of the opposti angle. The center of the excircles are called the excenters. Every triangle has three excirles.

The excircles are not necessarily tangent to the incircle.

Finally the sketch of the nine point circle will be overlayed onto triangle ABC.

The nine point circle is almost on top of the incircle of triangle ABC. The nine point circle touches the incircle and all three excircles.