# Centroid proof

## 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

mfb
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.
Andrax said:
phitagors
Pythagoras?

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

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mfb
Mentor
I think this problem statement does not make sense.

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

tiny-tim
Science Advisor
Homework Helper
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 )

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
Mentor
(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.