Difference between revisions of "2011 AIME I Problems/Problem 10"
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Revision as of 07:59, 29 March 2011
Problem
The probability that a set of three distinct vertices chosen at random from among the vertices of a regular n-gon determine an obtuse triangle is . Find the sum of all possible values of
.
Solution
This is not complete and may not be correct.
triangle is obtuse there exists
consecutive points that are not chosen. (i.e. all 3 points of the triangle are on the same half of the n-gon.
The probability of this happening is obviously lesser than , but
. Thus there is no such possible n-gon?
See also
2011 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |