Proving the Centroid of ABC Triangle

[Andrax]

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 don't know 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=..

 

[mfb]

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.

phitagors

Pythagoras?

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

 

[Andrax]

http://i48.tinypic.com/2u43dyv.jpg
so i wrote the exercise here hope it's clear now and sorry

 

[mfb]

I think this problem statement does not make sense.

 

[Andrax]

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

 

[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 )

 

[Andrax]

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 )

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

 

[mfb]

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

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