Question

If G be the centroid of a triangle ABC, prove that:

AB²+BC²+CA²=3(GA²+GB²+GC²)

Answer 1

Let A(b,c), B(0,0), C(a,0) be the coordinates of ΔABC

Then coordinates of centroid are

To prove:

Solving R.H.S

Therefore L.H.S = R.H.S proved.

Answer 2

   Here is your solution..