Incenter of a Triangle

Incenter of a Triangle

How to solve the incenter of a triangle problems: definition, properties, example, and its solution.

Definition

The incenter of a triangle is the center of the circle that inscribes the triangle.

The incenter of a triangle
is the center of the circle
that inscribes the triangle.

Properties

The distances between the incenter and each side of a triangle are the same.

So the distances between the incenter
and each side of a triangle
are the same.

Three angle bisectors of each triangle's interior angle meet at the incenter.

Three angle bisectors of each triangle's interior angle
meet at the incenter.

Example

Point O is the incenter of triangle ABC. Find the measure of angle OCB. The measure of angle A: 60, The measure of angle B: 50.

Point O is the incenter.

So OC (blue) is the angle bisector of ∠ACB.

Set m∠OCB = x.

Then 60 + 50 + 2x = 180.

Interior angles of a triangle