Solve Geometry Problems Using the Incenter of Any Given Triangle

In geometry, the point in a triangle where the angle bisectors of the triangle intersect is called the incenter. The following practice questions test your skills at finding the incenter of a given triangle.

Practice Questions

Point I is the incenter of triangle CEN. Use the following figure and the given information to solve the problems.

1. If

   

2. If

   

   is represented by 2c, and

   

   is represented by 2b + c, find the value of b.

Answers and Explanations

1. 26 degrees

   The incenter of a triangle is the point where the bisectors of each angle of the triangle intersect. A bisector divides an angle into two congruent angles.

   Find the measure of the third angle of triangle CEN and then cut the angle in half:

   

2. 4

   The incenter of a triangle is the point where the bisectors of each angle of the triangle intersect. A bisector divides an angle into two congruent angles.

   

Source: dummies.com