Question

If G be the centroid of a triangle ABC and P be any other point in the plane, prove that 

PA²+PB²+PC²=GA²+GB²+GC²+3GP²

Answer 1

Let A(0,0), B(a,0) and C(c,d) are the ordinates of triangle ABC

let P(x,y)

To prove:

Proof:

Solving R.H.S

L.H.S=R.H.S

Answer 2

If G be the centroid of a triangle ABC and P be any other point in the plane