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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

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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

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

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