Incenter (I)

The angle bisectors of a triangle are concurrent at a point called the incenter (I), the circumcenter is also the center of the inscribed circle of the triangle.

Furthermore, each angle bisector is concurrent with the external angle bisectors of the other two angles. The three points so created are the centres of the escribed circles of the triangle.

Proof of concurrency

To play with a GSP sketch that shows the incenter click here.