Question

Note: Your teacher will grade your response to questions 13–15 to ensure you receive proper credit for your answer.
What are the properties of the incenter of a triangle?
(2 points)

Answer 1

The properties of the incenter of a triangle are as follows:

1) The incenter is the point of concurrency of the three angle bisectors of the triangle. This means that the incenter is equidistant from all sides of the triangle.

2) The incenter is the center of the incircle, which is the largest circle that fits inside the triangle and touches all three sides. The incircle is tangent to the three sides of the triangle.

3) The incenter is equidistant from the three sides of the triangle. This means that the distances from the incenter to each side of the triangle are equal.

4) The incenter is the center of symmetry for the inscribed triangle, which is the triangle formed by connecting the points where the incircle touches the sides of the triangle.

5) The incenter is an important point in triangle geometry and is used in various geometric proofs and constructions.