The point of intersection of the right bisectors of a triangle is called

Options

A. in-centre
B. circumcentre
C. orthocentre
D. centroid

Answer

To solve the question, we need to identify the point of intersection of the right bisectors of a triangle. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- Consider a triangle \( XYZ \). This triangle has three sides: \( XY \), \( YZ \), and \( ZX \).

**Hint**: Visualize or draw a triangle to better understand the sides and vertices.

2. **Defining Right Bisectors**:
- The right bisector of a side of a triangle is a line that is perpendicular to that side and passes through the midpoint of the side. For example, if we take side \( XY \), the right bisector will be a line that is perpendicular to \( XY \) and intersects it at its midpoint.

**Hint**: Remember that a right bisector creates two equal segments on the side it bisects.

3. **Finding the Right Bisectors**:
- We can find the right bisectors for all three sides of the triangle:
- Right bisector of \( XY \)
- Right bisector of \( YZ \)
- Right bisector of \( ZX \)

**Hint**: Each right bisector should meet the respective side at a 90-degree angle.

4. **Intersection of Right Bisectors**:
- The point where all three right bisectors intersect is a special point in the triangle. This point is equidistant from all three vertices of the triangle.

**Hint**: Think about how this point relates to the triangle's vertices.

5. **Identifying the Special Point**:
- The point of intersection of the right bisectors is known as the **Circumcenter** of the triangle. This is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

**Hint**: Recall that the circumcenter can be inside, outside, or on the triangle depending on the type of triangle (acute, obtuse, or right).

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