The equidistant point from the vertices of a triangle is called its :

Options

A. Centroid
B. Incentre
C. Circumcentre
D. Orthocentre

Answer

To solve the question "The equidistant point from the vertices of a triangle is called its:", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- Start by visualizing or drawing a triangle with vertices labeled as A, B, and C.

2. **Identifying the Equidistant Point**:
- We need to find a point that is equidistant from all three vertices (A, B, and C) of the triangle.

3. **Defining the Point**:
- Let’s denote the point that is equidistant from A, B, and C as point O. This means that the distance from O to A (OA), O to B (OB), and O to C (OC) are all equal.

4. **Understanding the Circumcircle**:
- If we draw a circle that passes through all three vertices A, B, and C, the center of this circle is the point O. This circle is known as the circumcircle of the triangle.

5. **Naming the Point**:
- The point O, which is equidistant from the vertices of the triangle, is called the **Circumcenter** of the triangle.

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

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