The incenter of a triangle is the point on the interior of the triangle that is equidistant from the three sides.

The incenter of a triangle is denoted by I.

Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle.

Click here for a GSP script for a incenter given any three points (the vertices of the triangle).