Incenter
The incenter of a triangle or regular polygon is the point where the angle bisectors meet.
1. Triangles
In any triangle, the bisectors of the interior angles always meet at a single point  the incenter.
For more on this see Incenter of a triangle.
2. Regular polygons
The interior angles of any regular polygon always intersect at a single point  the incenter.
For more on this see Incenter of a polygon.
Irregular polygons have no incenter.
How to construct (draw) the incircle of a triangle with compass and straightedge or ruler. The three angle bisectors of any triangle always pass through its incenter. In this construction, we only use two, as this is sufficient to define the point where they intersect. We bisect the two angles and then draw a circle that just touches the triangles's sides. A Euclidean construction.
This page shows how to construct (draw) the incenter of a triangle with compass and straightedge or ruler. The incenter of a triangle is the point where all three angle bisectors always intersect, and is the center of the triangle's incircle. A Euclidean construction.
A method to find the coordinates on the incenter of a triangle given the coordinates of the three vertices.
The incenter of a regular polygon is the point where the interior angle bisectors intersect
An overview of the various centers of a triangle
Definition and properties of the incenter of a triangle
Definition and properties of the incircle of a triangle
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