Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        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`
6 years ago

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
G=a+b+c/3
GA=a-(a+b+c)/3=2a-b-c/3
similarly you can write for GB,GC,GO
GA2=(4a2+b2+c2-4a.b+b.c-4a.c)/9
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.
AKASH GOYAL

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

```
6 years ago
GOLU NAYAK
21 Points
```										if G is the centroid of the triangle ABC, prove by vector method thatGA+GB+GC=0
```
2 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Analytical Geometry

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details