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If G is the centroid of a triangle ABC, prove that 

(i)  AB2+BC2+CA2=3(GA2+GB2+GC2

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Let A(x1,y1),B(x2,y2)and C(x3,y3)be the vertices of △ABC.
Without the law of generality, assume the centroid oft he

AB2 + BC2 +CA2 =3(GA2 +GB2+GC2 )

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