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Sum to Cevian (Posted on 2016-09-03) Difficulty: 5 of 5

  
Let ABC be an equilateral triangle and P, a point in
the plane of ABC, not lying on any of the lines AB,
BC, or CA.

Let points A', B', and C' lie on lines BC, CA, and AB
respectively such that |AA'| = |BB'| = |CC'|.

Let points A", B", and C" lie on lines BC, CA, and
AB respectively such that PA" || AA', PB" || BB',
PC" || CC'.

Prove that

    |AA'| = SA*|PA"| + SB*|PB"| + SC*|PC"| ,

where SX = +1 if P and vertex X lie on the same side
                       of the sideline opposite vertex X,
               = -1 otherwise.


  

No Solution Yet Submitted by Bractals    
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