2017 AIME I Problems/Problem 1
Contents
[hide]Problem 1
Fifteen distinct points are designated on : the 3 vertices , , and ; other points on side ; other points on side ; and other points on side . Find the number of triangles with positive area whose vertices are among these points.
Solution
Every triangle is uniquely determined by 3 points. There are ways to choose 3 points, but that counts the degenerate triangles formed by choosing three points on a line. There are invalid cases on segment , invalid cases on segment , and invalid cases on segment for a total of invalid cases. The answer is thus .
Video Solution
https://youtu.be/BiiKzctXDJg ~Shreyas S
See Also
2017 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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