Every triangle has exactly three medians, one from each vertex, and they all intersect each other at a common point which is called centroid.

fig.5

In the fig.5, Let AD, BE and CF be the medians of ΔABC and point G be the centroid.

We know that-

Centroid of a Δ divides the medians of the Δ in the ratio 2:1.

Mid-point of side BC i.e. coordinates of point D is given by

Let the coordinates of the centroid G be (x,y).

Since centroid G divides the median AD in the ratio 2:1 i.e.

AG:GD = 2:1

∴ using section-formula, the coordinates of centroid is given by-

Now, according to question-

Centroid of ΔABC having vertices A(a, b), B(b, c) and C(c, a) is the origin.

Thus, the value of a + b + c is 0.