# International Mathematics Competition for University Students 2019

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IMC 2020
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## IMC2019: Day 2, Problem 10

Problem 10. $\displaystyle 2019$ points are chosen at random, independently, and distributed uniformly in the unit disc $\displaystyle \{(x,y)\in\RR^2\colon x^2+y^2\leq 1\}$. Let $\displaystyle C$ be the convex hull of the chosen points. Which probability is larger: that $\displaystyle C$ is a polygon with three vertices, or a polygon with four vertices?

Proposed by Fedor Petrov, St. Petersburg State University

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