# 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.

## Properties

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.

## Example

Point *O* is the incenter.

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

Set m∠*OCB* = *x*.

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

Interior angles of a triangle