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USAMO 1983 Problem 1 - Probability of disjoint triangle

Source: USAMO 1983 Problem 1

August 16, 2011
AMCUSA(J)MOUSAMOprobabilitycombinatorics unsolvedcombinatorics

Problem Statement

On a given circle, six points AA, BB, CC, DD, EE, and FF are chosen at random, independently and uniformly with respect to arc length. Determine the probability that the two triangles ABCABC and DEFDEF are disjoint, i.e., have no common points.
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