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Math Help - Tough analytical sum.

  1. #1
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    Lightbulb Tough analytical sum.

    Let z1, z2, z3 be the vertices of A,B,C of a triangle with the origin(O) the circumcenter. A transformation takes ABC to its circumcircle fixing the center and with the following property:-
    A point on AB be a.z1+(1-a)z2. Then after transformation it will be z1^a.z2^(1-a)
    Similar for BC and CA.
    This takes ABC to its circumcircle.
    By homothety with respect to O this transformation is defined for all other points in the plane also.
    Can anyone tell me what a line not passing through O changes to by this transformation??
    Last edited by mr fantastic; April 15th 2011 at 12:33 AM. Reason: Deleted begging in title, deleted email link in post.
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