Centroid proof

  • Thread starter Andrax
  • Start date
  • #1
117
0

Homework Statement



let ABC be a triangle where I divides angle BAC(angle A) => BAI=IAC
Prove that I is the centroid of (B,AC)and (C,AB)

Homework Equations


i think phitagors wil come in handy but dunno how to use it


The Attempt at a Solution


let ac = a and AB = b
aIB+bIC=0 (vectors)
aIC+aCB+bIC=(a+b)IC+aCB=..
 

Answers and Replies

  • #2
35,442
11,881
Did you copy the problem statement 1:1? It looks strange, phrased like that:

- the centroid is a point in a geometric shape, I would expect to see the triangle here. But (B,AC) and (C,AB) are strange ways to refer to a triangle
- I has to lie on the bisection of angle BAC, but nothing else is given. It could be anywhere, far away from the centroid.
Andrax said:
phitagors
Pythagoras?

I don't understand your notation at (3.).
 
  • #3
117
0
Last edited by a moderator:
  • #4
35,442
11,881
I think this problem statement does not make sense.
 
  • #5
117
0
It does... Dunno what I'm doing wrong
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hi Andrax! :smile:

Just use the sine formula. :wink:

(mfb, i think it means the centroid of a weight AC at B and a weight AB at C :biggrin:)
 
  • #7
117
0
Hi Andrax! :smile:

Just use the sine formula. :wink:

(mfb, i think it means the centroid of a weight AC at B and a weight AB at C :biggrin:)

thank you , with the' use of cos and sin i managed to prove that IG=IS anyway in class we used sin and cos + the S of the triangles
 
  • #8
35,442
11,881
(mfb, i think it means the centroid of a weight AC at B and a weight AB at C :biggrin:)
Ah, that makes sense.
We still need the requirement that I is on (BC), however.
 

Related Threads on Centroid proof

  • Last Post
Replies
7
Views
7K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
2K
Replies
6
Views
715
Replies
13
Views
1K
Replies
3
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
574
Top