The medians of any triangle are concurrent and that the point of concurrency divides each one of them in the ratio **2:1**.

Consider the triangle as shown in the diagram and suppose that , and be the vertices of the given triangle . As we know that median is defined as the line segment joining the vertex of triangle to the midpoint to the opposite side of the triangle.

Now suppose that , and are the midpoints of the sides of the triangle , so these midpoints can be calculate using midpoint formula as following:

Midpoint of the side is

Midpoint of the side is

Midpoint of the side is

Consider be the point intersection of the three medians of the triangle .

First we find the coordinates of the point with respect to median , since point divides the median in the ration , i.e. . To find the point using division formula or ratio formula (internal division).

Let and

Second we find the coordinates of the point with respect to median , since point divides the median in the ration , i.e. . To find the point using division formula or ratio formula (internal division).

Let and

Similarly, coordinates of with respect to .

Hence, the medians of a triangle are concurrent and its point of concurrency is