Problem Set Workbook
Access the downloadable workbook for 2012 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2012 USAJMO Day 1 math contest by visiting Random Math USAJMO Day 1 2012 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2012 USAJMO Day 1 problems, please refer below:
Problem 1:Given a triangle , let and be points on segments and , respectively, such that . Let and be distinct points on segment such that lies between and , and . Prove that are concyclic (in other words, these four points lie on a circle).
Solution:
Problem 2:Find all integers such that among any positive real numbers with
there exist three that are the side lengths of an acute triangle.
Solution:
Problem 3: Let be positive real numbers. Prove that
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions