2014 USAJMO Problems/Problem 2
Let be a non-equilateral, acute triangle with $\angle A=60\textdegrees$ (Error compiling LaTeX. ! Undefined control sequence.), 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 .
We draw a diagram to not lose points: