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Collinear Points (Posted on 2016-08-19) Difficulty: 3 of 5

  
Let points L, M, and N be on the sidelines BC, CA, and AB
of ΔABC respectively with AN = x*NB, BL = y*LC, and
CM = z*MA ( where XY denotes the vector from point X to
point Y ). Prove that

   If x*y*z = -1, then points L, M, and N are collinear.
  

No Solution Yet Submitted by Bractals    
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