Triangle: Incenter

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

Definition

Definition

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

Property

Property

Three angle bisectors of the interior angles
meet at the incenter.

Example

Example

Solution

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.