# Centroid proof

1. Jan 4, 2013

### Andrax

1. The problem statement, all variables and given/known data

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)

2. Relevant equations
i think phitagors wil come in handy but dunno how to use it

3. The attempt at a solution
let ac = a and AB = b
aIB+bIC=0 (vectors)
aIC+aCB+bIC=(a+b)IC+aCB=..

2. Jan 4, 2013

### Staff: Mentor

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.
Pythagoras?

I don't understand your notation at (3.).

3. Jan 4, 2013

### Andrax

Last edited by a moderator: Jan 4, 2013
4. Jan 4, 2013

### Staff: Mentor

I think this problem statement does not make sense.

5. Jan 4, 2013

### Andrax

It does... Dunno what I'm doing wrong

6. Jan 4, 2013

### tiny-tim

Hi Andrax!

Just use the sine formula.

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

7. Jan 5, 2013

### Andrax

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. Jan 5, 2013

### Staff: Mentor

Ah, that makes sense.
We still need the requirement that I is on (BC), however.