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Grade: 12


If G is the centroid of the triangle ABC and O is any other point in the plane then prove that (OA) 2 + (OB) 2 + (OC) 2 =(GA) 2 + (GB) 2 + (GC) 2 + 3(GO) 2

9 years ago

Answers : (2)

AKASH GOYAL AskiitiansExpert-IITD
419 Points

Dear Sohan

You can do it by coordinates and vectors both methods

vector method is simple and involves less variables

assume o as origin

Position vectors of A,B,C as a,b,c respectively

OA=a, OB=b,OC=c



similarly you can write for GB,GC,GO


similarly write for others and just calculate the expression

similarly using coordinate 

you can take o as (0,0)and A,B,C as (x1,y1),(x2,y2)and (x3,y3)

G will be ((x1+x2+x3)/3 , (y1+y2+y3)/3)

and using distance formula solve the expressions on LHS and RHS


 All the best.                                                          


AskiitiansExpert-IIT Delhi


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9 years ago
21 Points
if G is the centroid of the triangle ABC, prove by vector method that
5 years ago
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