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?
The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It has several properties:
1. 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.
2. The incenter is the center of the inscribed circle, also known as the incircle, which is the largest circle that can fit inside the triangle.
3. The incenter of a triangle is also the point of concurrency of the angle bisectors. This means that if you draw the angle bisectors of each angle in the triangle, they will all intersect at the incenter.
4. The incenter is always inside the triangle. It is never outside or on the triangle.
These properties make the incenter an important point of reference in triangle geometry, and it is often used in various geometric constructions and calculations.