The point where the all three medians of a triangle meet is called

Options

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

Answer

To solve the question, we need to identify the point where all three medians of a triangle meet. Here’s a step-by-step solution:

### Step 1: Understand the Definition of Medians
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Each triangle has three medians.

**Hint:** Remember that a median connects a vertex to the midpoint of the opposite side.

### Step 2: Identify the Meeting Point of Medians
The point where all three medians intersect is known as the centroid of the triangle. The centroid is the balance point of the triangle and divides each median into two segments, with the segment connecting the vertex to the centroid being twice the length of the segment connecting the centroid to the midpoint of the side.

**Hint:** The centroid is a special point that balances the triangle.

### Step 3: Review the Options Given
The options provided in the question are:
1. Centroid
2. In-center
3. Circum-center
4. Ortho-center

We need to determine which of these points is the centroid.

**Hint:** Recall the definitions of the other points: the in-center is where the angle bisectors meet, the circum-center is where the perpendicular bisectors meet, and the ortho-center is where the altitudes meet.

### Step 4: Conclusion
From the definitions and the properties of the triangle, we conclude that the point where all three medians meet is called the **centroid**.

**Final Answer:** The point where all three medians of a triangle meet is called the **centroid**.