Angle Bisectors & Incenter Investigation

In the app below, you can change the size of the triangle by moving any one (or more) of its vertices. You can also alter the size of the angle in the lower left corner by using the smaller slider. (You can also zoom in/out.)
1.
The point you see inside the triangle is called the INCENTER of this triangle. Notice there are 3 equal distances in this triangle. How would you describe these equal distances in your own words? That is, each of these distances is the distance from the _________ to ___________?
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2.
What is so special about the circle with respect to the sides of the triangle?
Font sizeFont size
Very smallSmallNormalBigVery big
Bold [ctrl+b]
Italic [ctrl+i]
Underline [ctrl+u]
Strike
Superscript
Subscript
Font color
Auto
Justify
Align left
Align right
Align center
• Unordered list
1. Ordered list
Quote [ctrl+shift+3]
[code]Code [ctrl+shift+4]
Insert table
Remove Format
Insert image [ctrl+shift+1]
Insert icons of GeoGebra tools
[bbcode]
Text tools
Insert Math
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Information: Angle Bisectors & Incenter Investigation