Incenter (I)

The incenter I is the intersection of the internal angle bisectors. It is the center of the incircle, tangent to all three sides.

Keywords: incenter, angle bisector, incircle, tangent, triangle centers

Prerequisites: triangle · Difficulty: beginner

The incenter is a special point that is the same distance from all three sides of the triangle.

The Incircle

Because the incenter is equally far from each side, you can draw a circle inside the triangle that perfectly touches all three sides without going over. This is the biggest possible circle that can fit inside the triangle, and it's called the incircle. The incenter is the exact center of this circle.

How do we find it?

To find the incenter, we draw the angle bisectors of the triangle's corners (vertices).

An angle bisector is a line that cuts an angle into two smaller, equal angles.

Each triangle has three angles, so it has three angle bisectors. They all meet at a single point: the incenter!

Fun Fact

The incenter is always located inside the triangle, no matter what shape the triangle is.