8.2 Incenter (I) - concurrent at angle bisectors - incenter incircle inradius
Finding the incenter and creating the incircle of a triangle: Remember that the incenter is equidistant from the SIDES of the triangle.
The distance from a point to a line is measured using the line that is PERPENDICULAR to the side passing through the point. This does NOT mean it bisects the opposite side (it could, but it doesn't have to).
A point that is equidistant from two sides of a triangle lies on the angle bisector. Why?
When would we need this?
A farmer in Colorado is installing a circular sprinkler (a sprinkler whose spray makes a perfect circle) to water his crops. His land is in the shape of a triangle and is surrounded by neighboring farms. The sprinkler should be placed so as to cover as much of his land as possible without spraying his neighbors' land. Where should he place his sprinkler?