[color=#000000]Recall that 3 or more lines are said to be concurrent if and only if they intersect at exactly one point. [br][br]The angle bisectors of a triangle's 3 interior angles are all concurrent. [br]Their point of concurrency is called the I[b]NCENTER[/b] of the triangle. [br]In the applet below, [b]point I [/b]is the triangle's [b]INCENTER[/b]. [br]Use the tools of GeoGebra in the applet below to complete the activity below the applet. [br][i]Be sure to answer each question fully as you proceed. [/i][/color]

[color=#000000][b]Directions: [br][/b][/color][color=#000000]1) Click the checkbox that says "Drop Perpendicular Segments from I to sides. [br][/color][color=#000000]2) [/color][color=#000000]Now, use the [b]Distance[/b] tool to measure and display the lengths [i]IG[/i], [i]IH[/i], and [i]IJ[/i]. What do you notice?[br][br]3) Experiment a bit by moving any one (or more) of the triangle's vertices around[br] Does your initial observation in (2) still hold true? Why is this? [br] (If you need a hint, refer back to the worksheet found [url=https://tube.geogebra.org/m/tU3ZqhjN]here[/url]. [br][br][/color][color=#000000]4) Construct a circle centered at I that passes through [i]G[/i]. What else do you notice[br] Experiment by moving any one (or more) of the triangle's vertices around. [br] This circle is said to be the triangle's [i]incircle[/i], or [i]inscribed circle. [br][/i] It is the largest possible circle one can draw [i]inside[/i] this triangle.[br] Why, according to your results from (2), is this possible? [br][br]5) Do the angle bisectors of a triangle's interior angles also bisect the sides opposite theses angles? [br] Use the [b]Distance[/b] tool to help you answer this question.[br][br][/color][color=#000000]6) Is it ever possible for a triangle's [b]INCENTER[/b] to lie OUTSIDE the triangle[br] If so, under what condition(s) will this occur? [br][br]7) Is it ever possible for a triangle's [b]INCENTER[/b] to lie ON the triangle itself?[br] If so, under what condition(s) will this occur? [/color]