Difference between revisions of "1983 USAMO Problems/Problem 1"
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| − | + | ==Problem== | |
| + | If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three? | ||
| + | ==Hint== | ||
| + | First choose six points on the circumference on a circle. What is the probability that selecting three random points will yield a triangle that is disjoint from the triangle formed by the other three points? | ||
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| + | |||
| + | |||
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| + | ==Solution== | ||
| + | The probability in the hint equals <math>\frac{3}{10}</math>, and that is the answer! | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 14:28, 19 April 2014
Problem
If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three?
Hint
First choose six points on the circumference on a circle. What is the probability that selecting three random points will yield a triangle that is disjoint from the triangle formed by the other three points?
Solution
The probability in the hint equals 
, and that is the answer!
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
