2001 AMC 12 Problems/Problem 14
Contents
[hide]Problem
Given the nine-sided regular polygon , how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set ?
Solution
Each of the pairs of vertices determines two equilateral triangles — one facing towards the center, and one outwards — for a total of 72 triangles. However, the three triangles , , and are each counted 3 times, resulting in an overcount of 6. Thus, there are distinct equilateral triangles.
Video Solution
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.