MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
SOHAN SARANGI 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

6 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


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


AskiitiansExpert-IIT Delhi


 


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.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


 

6 years ago
GOLU NAYAK
21 Points
										
if G is the centroid of the triangle ABC, prove by vector method that
GA+GB+GC=0
one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details