The largest circle that fits inside a polygon and is tangent to (touches without crossing) all its sides.
• it exists for triangles, regular polygons, and some other special shapes, but not all polygons.
• in regular polygons, the radius of the incircle is called the apothem.
Below is the incircle of a triangle (try dragging the points):
../geometry/images/triangle.js?mode=incircle