2014 USAJMO Problems/Problem 2
Revision as of 18:12, 29 April 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== Let <math>\triangle{ABC}</math> be a non-equilateral, acute triangle with <math>\angle A=60\textdegrees</math>, and let <math>O</math> and <math>H</math> denote the c...")
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 
.
