The Incenter of a triangle

The point where the three angle bisectors of a triangle meet.
One of a triangle's points of concurrency.
Try this Drag the orange dots on each vertex to reshape the triangle. Note the way the three angle bisectors always meet at the incenter.

One of several centers the triangle can have, the incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle - the largest circle that will fit inside the triangle.

Properties of the incenter

Center of the incircle The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. See Incircle of a Triangle.
Always inside the triangle The triangle's incenter is always inside the triangle. Adjust the triangle above by dragging any vertex and see that it will never go outside the triangle

Finding the incenter of a triangle

It is possible to find the incenter of a triangle using a compass and straightedge.
See Constructing the the incenter of a triangle.

Coordinate geometry

If you know the coordinates of the triangle's vertices, you can calculate the coordinates of the incenter. See Coordinates of incenter.

Summary of triangle centers

There are many types of triangle centers. Below are four of the most common.
Incenter Located at intersection of the angle bisectors.
See Triangle incenter definition
Circumcenter Located at intersection of the perpendicular bisectors of the sides.
See Triangle circumcenter definition
Centroid Located at intersection of medians.
See Centroid of a triangle
Orthocenter Located at intersection of the altitudes of the triangle.
See Orthocenter of a triangle
In the case of an equilateral triangle, all four of the above centers occur at the same point.

Other triangle topics


Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises