Geometry · Triangles & Congruence
Incenter
HSG-CO.C.10
Definition
The point where a triangle's three angle bisectors meet, equidistant from the sides.
Examples
- The incenter I is equidistant from all three sides of triangle ABC — the radius of the inscribed circle.
- The incenter is always inside the triangle, unlike the circumcenter, which can fall outside.
Key rule
The incenter is the center of the triangle's inscribed circle (incircle), tangent to all three sides.
Memory hook
Where the angle bisectors meet — center of the circle inside the triangle.