Which of the following is equidistant from the vertices of a triangle ?

Options

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

Answer

To determine which point is equidistant from the vertices of a triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Triangle and its Vertices**:
- Consider a triangle with vertices labeled as A, B, and C.

2. **Identify the Concept of Equidistance**:
- A point that is equidistant from the vertices of a triangle is a point that has the same distance to each of the triangle's vertices.

3. **Introduce the Circumcenter**:
- The point that is equidistant from all three vertices of a triangle is known as the **Circumcenter**.

4. **Visualize the Circumcenter**:
- To find the circumcenter, you can draw the perpendicular bisectors of each side of the triangle. The point where these bisectors intersect is the circumcenter.

5. **Conclusion**:
- Therefore, the circumcenter is the point that is equidistant from the vertices A, B, and C of the triangle.

### Final Answer:
The point that is equidistant from the vertices of a triangle is the **Circumcenter**.

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