Incenter Exploration (B)
3 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. In the applet below, point I is the triangle's INCENTER. 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) Click the checkbox that says "Drop Perpendicular Segments from I to sides. 2) Now, use the Distance tool to measure and display the lengths IG, IH, and IJ. What do you notice? 3) Experiment a bit by moving any one (or more) of the triangle's vertices around Does your initial observation in (2) still hold true? Why is this? 4) Do the angle bisectors of a triangle's interior angles also bisect the sides opposite theses angles? Use the Distance tool to help you answer this question. 5) Is it ever possible for a triangle's INCENTER to lie OUTSIDE the triangle If so, under what condition(s) will this occur? 6) Is it ever possible for a triangle's INCENTER to lie ON the triangle itself? If so, under what condition(s) will this occur?