1973 USAMO Problems/Problem 3

Problem

Three distinct vertices are chosen at random from the vertices of a given regular polygon of sides. If all such choices are equally likely, what is the probability that the center of the given polygon lies in the interior of the triangle determined by the three chosen random points?

Solution

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See also

1973 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions