The point at which the perpendicular bisectors of the sides of a triangle intersect is known as ________.

Options

A. circum-centre
B. orthocentere
C. centroid
D. in-centre

Answer

To solve the question, we need to identify the point at which the perpendicular bisectors of the sides of a triangle intersect. Let's go through the steps to arrive at the answer.

### Step-by-Step Solution:

1. **Understanding Perpendicular Bisectors**:
- A perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a right angle (90 degrees).

2. **Identifying the Triangle**:
- Consider a triangle with vertices A, B, and C. We will denote the sides of the triangle as AB, BC, and AC.

3. **Finding Midpoints**:
- Calculate the midpoints of each side of the triangle:
- Midpoint of side BC: Let’s denote it as M1.
- Midpoint of side AC: Let’s denote it as M2.
- Midpoint of side AB: Let’s denote it as M3.

4. **Drawing Perpendicular Bisectors**:
- From each midpoint, draw a line that is perpendicular to the corresponding side:
- Draw the perpendicular bisector from M1 to side BC.
- Draw the perpendicular bisector from M2 to side AC.
- Draw the perpendicular bisector from M3 to side AB.

5. **Finding the Intersection Point**:
- The three perpendicular bisectors will intersect at a single point. Let’s denote this intersection point as O.

6. **Identifying the Name of the Point**:
- The point O, where all three perpendicular bisectors intersect, is known as the **Circumcenter** of the triangle.

### Final Answer:
The point at which the perpendicular bisectors of the sides of a triangle intersect is known as the **Circumcenter**.

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