# 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.

## Properties

Property 1:

The distances

between the incenter and each side

are the same.

Property 2:

Three angle bisectors of the triangle's interior angles

meet at the incenter.

Angles bisectors of a triangle - Definition

## Example

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* = 2*x*.

The interior angles of △*ABC* are

60º, 50º, and 2*x*º.

So 60 + 50 + 2*x* = 180.

Interior angles of a triangle

60 + 50 = 110

Move 110 to the right side.

Then 2*x* = 70.

Divide both sides by 2.

Then *x* = 35.