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.