Geometry (15) what are the properties of the incenter of a triangle?

The incenter of a triangle is equidistant from all sides of the triangle

The incenter is the center of the biggest circle that can be drawn in the triangle, and is called incircle

The incircle will be tangent to all sides of the triangle.

Observation:
In an equilateral triangle the incenter, circumcenter, and centroid are all the same