5.1 Incenter
The incenter of a triangle is a point of concurrency for the three angle bisectors of the angles of the triangle. In the triangle ABC below, each of the 3 angles has been bisected. Modify the construction in order to examine the incenter of different triangles and explore the properties of the incenter.
Task 1
Modify the shape of the triangle by dragging its vertices with the mouse. Change the measures of the angles, the lengths of the sides, and the location of the incenter. Move the vertices in multiple locations to observe changes when...
a) all angles are acute.
b) one angle is obtuse.
c) one angle is a right angle.
and then answer the questions below.
Where is the incenter when the triangle is acute?
Where is the incenter when the triangle is obtuse?
Where is the incenter when the triangle is a right triangle?
The incenter is the center of the blue circle. No matter what type of triangle is constructed, what do you notice about the relationship between the blue circle and the sides of the triangle? What does that tell you about the relationship between the incenter and the sides of the triangle?