Copy of Incenter + Incircle Action (V2)!

In the applet below, you can change the size of the triangle by moving any one (or more) of its vertices.[br][color=#ff00ff][b][br]You can also alter the size of the (soon to appear) pink angle by using the pink slider. [br][/b][/color](You can also zoom in/out.)
1.
What vocabulary term would you ascribe to the 3 gray segments WITHIN THIS TRIANGLE?
2.
How do these 3 gray segments intersect? Describe.
3.
[b][color=#1e84cc]The light blue point is called the triangle's INCENTER.[/color][/b] [br]Notice there are 3 equal distances in this triangle. How would you describe these equal distances in your own words? [br][br]That is, each of these distances is the distance from _________ to ___________?
4.
Why do your observation(s) and response to (3) above hold true? What previously learned theorem justifies this?
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