Incenter
Definition of Incenter

• Incenter is the Center of a Circle inscribed in a triangle. It is the Point of Intersection of all the Angle bisectors of a triangle.

More about Incenter

• Incenter of a Triangle is equidistant from the sides of the triangle.
• The Cartesian Coordinates of the incenter, with the vertices of the Triangle being , and lengths of the opposite sides of the Triangle being a, b, and c, are given by .

Example of Incenter

• The Incenter for the above figure is “I” as it is the Center of the Circle inscribed in a triangle.So, “I” is the Incenter for the above figure.

Solved Example on Incenter

Select the correct statements.
I. The Triangle is inscribed in the circle.
II. I is called incenter.
III. Angle ABI is always equal to Angle BAI.
IV. BI is called inradius.

Choices:
A. Only IV
B. I and II
C. Only II
D. I and IV
Correct Answer: C
Solution:
Step 1: Here, 'I is called incenter' is the only correct statement.
[The point of concurrency of the three Angle bisectors of a Triangle is called the incenter.]

Related Terms for Incenter

• Bisectors
• Point of Intersection
• Triangle

Additional Links for Incenter

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