[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][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: [/b][br][br][/color][left][color=#000000]1) In the applet above [/color][color=#38761d]construct a line passing through I and is perpendicular to [i]AB[/i][/color][color=#000000]. [br]2) Use the [/color][b][color=#000000]Intersect[/color][/b][color=#000000] tool to plot and label a point [/color][i]G[/i][color=#000000] where [/color][color=#38761d]the line you constructed in (1)[/color][color=#000000] intersects [/color][i][/i][color=#000000][i]AB[/i].[/color][color=#000000][br]3) [/color][color=#38761d]Construct a line that passes through I and is perpendicular to [i]BC[/i].[/color][color=#000000] [br][/color][color=#000000]4) Plot and label a point [i]H[/i] where [/color][color=#38761d]the line you constructed in (3)[/color][color=#000000] intersects [i]BC[/i].[/color][br][color=#000000]5) [/color][color=#38761d]Construct a line that passes through I and is perpendicular to [i]A[/i][i]C[/i]. [/color][color=#000000][br][/color][color=#000000]6) Plot and label a point [/color][i]J[/i][color=#000000] where [/color][color=#38761d]the line you constructed in (5)[/color][color=#000000] intersects [/color][i][color=#000000]AC[/color][/i][color=#000000]. [br]7) 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][br]8) Experiment a bit by moving any one (or more) of the triangle's vertices around[br] Does your initial observation in (7) still hold true? [br] Why is this? (If you need a hint, refer back to the worksheet found [url=https://tube.geogebra.org/m/tU3ZqhjN]here[/url]. [/color][/left][color=#000000][br]9) 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[/i]. [br] It is the largest possible circle one can draw [i]inside[/i] this triangle. [br] Why, according to your results from (7) is this possible? [br][br]10) 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. [/color][br][br][color=#000000]11) 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]12) 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]