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Centroid proof

  1. Jan 4, 2013 #1
    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. jcsd
  3. Jan 4, 2013 #2

    mfb

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    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.).
     
  4. Jan 4, 2013 #3
    Last edited by a moderator: Jan 4, 2013
  5. Jan 4, 2013 #4

    mfb

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    I think this problem statement does not make sense.
     
  6. Jan 4, 2013 #5
    It does... Dunno what I'm doing wrong
     
  7. Jan 4, 2013 #6

    tiny-tim

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    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:)
     
  8. Jan 5, 2013 #7
    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
     
  9. Jan 5, 2013 #8

    mfb

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