If G and G` be hte centroid of the triangle ABC and triangle A`B`C` respectively then AA`+BB`+CC`=

Dear palllavi

let O is the origin

then OG  =( OA +OB +OC)/3

 

and OG' = (OA' + OB ' OC')/3

 

subtract

  OG -OG'=  ( OA +OB +OC)/3 - (OA' + OB ' OC')/3   

 GG'  = (AA' + BB' + CC')/3

AA`+BB`+CC`= 3GG'

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