What do you notice about the three angle bisectors?[br][br]What happens when you manipulate the triangle so it is acute? Right? Obtuse?[br][br]Construct a perpendicular to one of the sides through the point you created with the angle bisectors then draw a circle with center at the intersection of the angle bisectors and edge at the place where the new perpendicular line intersects the side. What do you notice?
The angle bisectors meet at one point, this point is called the [b]incenter[/b] and it is the center of the [b]incircle[/b]. The incircle is a circle [b]inscribed[/b] within the triangle which means it touches the each side of the triangle exactly once.[br][br]The shape of the triangle does not matter, the incenter is always inside the triangle towards the center.[br][br]The circle you drew should touch each side of the triangle exactly once, we all this [b]tangent, [/b]when a line touches a curve in a glancing blow and "bounces" off.