If AD, BE and CF are the medians of a △ABC then (AD2+BE2+CF2):(BC2+CA2+AB2) is equal to
3:4
AB2+AC2=2(AD2+BD2)
⇒c2+b22−a24=AD2
Similarly, a2+b22−c24=CF2 and a2+c22−a2+c24=BE2
Adding a2+b2+c2−(a2+b2+c24)=AD2+BE2+CF2
⇒(AD2+BE2+CF2):(a2+b2+c2)=3:4