MathDB

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Part of 2018 Costa Rica - Final Round

Problems(1)

probability of 2 segments from 10 points on a circle intersect

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.1

9/20/2021
There are 1010 points on a circle and all possible segments are drawn on the which two of these points are the endpoints. Determine the probability that selecting two segments randomly, they intersect at some point (it could be on the circumference).
geometrycombinatorial geometrycombinatorics