The point where the interior angle bisectors intersect.

Try this
Drag any orange dot and change the number of sides. Note where the bisectors of the interior angles meet.

If you bisect the interior angles of a regular polygon, the bisectors will always converge at the same point - called the incenter of the polygon. The incenter is also the center of:

- The incircle - the largest circle that will fit inside the polygon
- The circumcircle - the circle that passes through every vertex.

For irregular polygons - where the side lengths and interior angles are all different - the angle bisectors do not meet at a single point, so irregular polygons have no incenter.

Regular polygons (and all triangles) have other centers too:

- Circumcenter - the point where the three perpendicular bisectors of the sides meet.
- Centroid - the point where the altitudes meet.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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