2014 USAJMO Problems/Problem 2
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Problem
Let 
be a non-equilateral, acute triangle with $\angle A=60\textdegrees$ (Error compiling LaTeX. Unknown error_msg), and let 
and 
denote the circumcenter and orthocenter of , respectively.
(a) Prove that line 
intersects both segments 
and 
.
(b) Line intersects segments and at 
and 
, respectively. Denote by 
and 
the respective areas of triangle 
and quadrilateral 
. Determine the range of possible values for 
.
