In an equilateral triangle, the incentre, circumcentre, orthocentre and centroid are :

Options

A. concylic
B. coincident
C. collinear
D. none of these

Answer

To solve the question regarding the properties of an equilateral triangle, we will analyze the positions of the incenter, circumcenter, orthocenter, and centroid step by step.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- An equilateral triangle has all three sides equal and all three angles equal (each measuring 60 degrees).
- Let's denote the vertices of the triangle as \( A \), \( B \), and \( C \).

2. **Identifying Key Points**:
- **Incenter**: The point where the angle bisectors of the triangle intersect. It is also the center of the inscribed circle.
- **Circumcenter**: The point where the perpendicular bisectors of the sides intersect. It is the center of the circumscribed circle.
- **Orthocenter**: The point where the altitudes of the triangle intersect.
- **Centroid**: The point where the medians of the triangle intersect.

3. **Properties of Equilateral Triangle**:
- In an equilateral triangle, the incenter, circumcenter, orthocenter, and centroid all coincide at the same point. This is because:
- The angle bisectors, medians, and altitudes are all the same lines due to the symmetry of the triangle.
- Therefore, all four points are located at the same position.

4. **Conclusion**:
- Since all four points (incenter, circumcenter, orthocenter, and centroid) coincide, the answer to the question is that they are "coincident".

### Final Answer:
The incenter, circumcenter, orthocenter, and centroid of an equilateral triangle are coincident.

---