The point of intersection of the angle bisectors of a triangle is :

Options

A. orthocentre
B. centroid
C. incentre
D. circumcenter

Answer

To find the point of intersection of the angle bisectors of a triangle, we can follow these steps:

1. **Understand the Definition of an Angle Bisector**: An angle bisector is a line that divides an angle into two equal parts. In a triangle, each vertex has an angle, and the angle bisector of that vertex will split it into two equal angles.

2. **Identify the Angle Bisectors**: In a triangle, there are three angles, and thus three angle bisectors. Let's denote the triangle as ABC, where A, B, and C are the vertices. The angle bisectors would be:
- The angle bisector of angle A (dividing it into two equal angles).
- The angle bisector of angle B (dividing it into two equal angles).
- The angle bisector of angle C (dividing it into two equal angles).

3. **Locate the Point of Intersection**: The three angle bisectors will intersect at a single point inside the triangle. This point is special because it is equidistant from all three sides of the triangle.

4. **Name the Point**: The point where the three angle bisectors of a triangle intersect is known as the **Incenter** of the triangle. The Incenter is also the center of the circle that can be inscribed within the triangle (the incircle).

5. **Conclusion**: Therefore, the point of intersection of the angle bisectors of a triangle is called the Incenter.

### Final Answer:
The point of intersection of the angle bisectors of a triangle is called the **Incenter**.

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