1985 OIM Problems/Problem 6
Problem
Given triangle 
, we consider the points 
, 
, and 
of lines 
, 
, and 
respectively. If lines 
, 
, and 
all pass through the center 
of the circumference of triangle , which radius is 
, prove:
![\[\frac{1}{AD}+\frac{1}{BE}+\frac{1}{CE}=\frac{2}{r}\]](http://latex.artofproblemsolving.com/6/1/5/615ea4eb1cd1edd46fccfb3b95cee60d42c21b01.png)
Solution
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