We know that the medians of the triangle are concurrent.
The point of concurrence of the three medians is the centroid of the triangle.
In the figure given above, \(G\) is the centroid of \(\triangle ABC\).
Properties of centroids
Based on the location of the centroid, the centroid exhibits the following properties:
[Note: Refer to the image given below for a better understanding.]
1. The centroid is always located inside the circle.
2. When a triangular plane surface is considered, the centroid acts as the centre of gravity.
3. The medians and the centroid together divide the triangle into three triangles of equal area.
In the figure we refer to, the three triangles of equal area are \(\triangle CGB\), \(\triangle GAB\), and \(\triangle AGC\).
The centroid always divides the median into two-parts to one. That is, the centroid divides the median in the ratio \(2 : 1\). The portion between the vertex and the centroid on the median occupies two parts of the median, while the portion between the centroid and the other end of the median occupies one part of the median.