# Triangle: Incenter

How to use the property of the incenter of a triangle: definition, property, 1 example, and its solution.

## Definition

The incenter of a triangle

is the center of the circle

that inscribes the outer triangle.

## Property

Three angle bisectors of the interior angles

meet at the incenter.

## Example

Solution

Solution (Detail)

It says

point O is the incenter.

So, to remind yourself that

point O is the incenter,

lightly draw the inscribed circle.

Then OC is the angle bisector of ∠C.

Set ∠OCB xº.

∠OCB and ∠OCA are congruent.

So ∠OCA is also xº.

∠A is 60º.

∠B is 50º.

∠C is, x + x, 2xº.

So 60 + 50 + 2x = 180.

Triangle: Interior Angles

60 + 50 = 110

Move 110 to the right side.

Then 2x = 70.

Divide both sides by 2.

Then x = 35.

So x = 35.