2014 USAJMO Problems
Contents
[hide]Day 1
Problem 1
Let , , be real numbers greater than or equal to . Prove that Solution
Problem 2
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 .
Problem 3
Let be the set of integers. Find all functions such that for all with .