Problem Set Workbook
Access the downloadable workbook for 2001 USAMO problems here.
Discussion Forum
Engage in discussion about the 2001 USAMO math contest by visiting Random Math USAMO 2001 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2001 USAMO problems, please refer below:
Problem 4: Let be a point in the plane of triangle such that the segments , and are the sides of an obtuse triangle. Assume that in this triangle the obtuse angle opposes the side congruent to . Prove that is acute.
Solution:
Problem 5: Let be a set of integers (not necessarily positive) such that
Prove that is the set of all integers.
Solution:
Problem 6: Each point in the plane is assigned a real number such that, for any triangle, the number at the center of its inscribed circle is equal to the arithmetic mean of the three numbers at its vertices. Prove that all points in the plane are assigned the same number.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions