1) If G be the centroid of a trianglt ABC AB2 + BC2 + CA2 = 3(GA 2+ GB2 + GC2)
2) Prove that AB2 + AC2 = 2( AO2 + OC2) where O is the mid point of BC
1) Without loss of generality you can take A as (-a,0) and B as (a,0).C can be taken as (x,y).This makes it simple.
2) Here also you can take B as (-a,0) and C as (a,0).O is the origin since it the midpoint of BC.A can be taken as (x,y).I am assuming that this is a different question from 1).
thanks