2015 OIM Problems/Problem 2
Problem
A line 
contains the points 
, 
, 
and 
in that order. Let 
be a point outside of such that 
. Prove that the bisector of 
cuts at a point 
such that
![\[\frac{1}{GA}+\frac{1}{GC}=\frac{1}{GB}+\frac{1}{GD}\]](http://latex.artofproblemsolving.com/0/e/9/0e96628b9cde3206ad485a3ca67769a739bdde9d.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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