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HMMT 2020 C8

  • Combinatorics
  • Answer

Let Γ1\Gamma_{1} and Γ2\Gamma_{2} be concentric circles with radii 1 and 2 , respectively. Four points are chosen on the circumference of Γ2\Gamma_{2} independently and uniformly at random, and are then connected to form a convex quadrilateral. What is the probability that the perimeter of this quadrilateral intersects Γ1\Gamma_{1} ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{22}{27}

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