Definition of "incircle"

To construct the incircle of ΔABC, we need the center of the circle and a pass-through point.

2003, Clark Kimberling, Geometry in Action: A Discovery Approach Using the Geometer's Sketchpad, page 16

Having constructed K, the incircle of the quadrilateral can be easily constructed since it is tangent to BA and BC.

2005, István Reiman, International Mathematical Olympiad: 1959-1975, page 51

For example, in Figure 4.2a only two edges of the polygon are tangent to the incircle. The other four edges do not even touch the incircle, but their extensions, shown by dotted lines, are tangent to the incircle.

2012, Tom M. Apostol, Mamikon A. Mnatsakanian, New Horizons in Geometry, Mathematical Association of America, page 106