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'| = S_A*|PA"| + S_B*|PB"| + S_C*|PC"| ,

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


  

There are no comments yet.