5.3. Incenter Exploration
Three or more lines are said to be CONCURRENT if and only if they intersect at exactly one point.
The angle bisectors of a triangle's 3 interior angles are all concurrent.
Their point of concurrency is called the INCENTER of the triangle.
Use the tools of GeoGebra in the applet below to complete the activity below the applet.
Be sure to answer each question fully as you proceed.
Directions:
1) Identify three angles bisectors. 2.) Identify the incenter.
3) Is it ever possible for a triangle's INCENTER to lie OUTSIDE the triangle? If so, under what condition(s) will this occur? 4) Is it ever possible for a triangle's INCENTER to lie ON the triangle itself? If so, under what condition(s) will this occur? 5) Measure the distance from the incenter to each of the sides of a triangle. You should have three measurements. Move the vertices around. What do you notice? 6) Write a conjecture about the distance from the incenter of a triangle to the three sides.