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

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the Terms**:
- First, we need to understand what angle bisectors are. An angle bisector of a triangle is a line that divides an angle into two equal parts.

2. **Identify the Points of Intersection**:
- In a triangle, there are several important points of intersection:
- **Orthocenter**: The intersection of the altitudes.
- **Centroid**: The intersection of the medians.
- **Incenter**: The intersection of the angle bisectors.
- **Circumcenter**: The intersection of the perpendicular bisectors.

3. **Focus on Angle Bisectors**:
- Since the question specifically asks about the angle bisectors, we will focus on the point where these bisectors intersect.

4. **Conclusion**:
- The point of intersection of the angle bisectors of a triangle is known as the **Incenter**. This point is equidistant from all three sides of the triangle.

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