Incenter of a Triangle

Incenter of a Triangle

How to find the incenter of a triangle: 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 are the same.

Property 1:

The distances
between the incenter and each side
are the same.

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

Property 2:

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

Angles bisectors of a triangle - Definition

Example

Point O is the incenter of triangle ABC. Find [measure of angle OCB]. [measure of angle A] = 60, [measure of angle B] = 50.

It says point O is the incenter.

So OC is the angle bisector of ∠ACB.

Set m∠OCB = x.

Then m∠OCA is also x.

So m∠ACB = 2x.

The interior angles of △ABC are
60º, 50º, and 2xº.

So 60 + 50 + 2x = 180.

Interior angles of a triangle

60 + 50 = 110

Move 110 to the right side.

Then 2x = 70.

Divide both sides by 2.

Then x = 35.