2025 AIME I Problems/Problem 12
Problem
The set of points in 
-dimensional coordinate space that lie in the plane 
whose coordinates satisfy the inequalities ![\[x-yz<y-zx<z-xy\]](http://latex.artofproblemsolving.com/8/2/9/82998ee0bab0aee5af1bd428ead1e25750b3a2b1.png)
forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form 
where 
and 
are positive integers and is not divisible by the square of any prime. Find 
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
