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 
, proof that:
$$ (Error compiling LaTeX. Unknown error_msg)\frac{1}{AD}+\frac{1}{BE}+\frac{1}{CE}=\frac{2}{r}
Solution
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