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Australian AMC 2024 - Senior Question 25

AMC AUSTRALIA · Australian AMC 2024 - Senior

Question 25

A solid regular tetrahedron of side length 2 is inscribed inside a hollow cylinder, so that two of its edges are diameters of the circular ends of the cylinder. What is the diameter of the largest sphere that can fit between the tetrahedron and the cylinder?

Question illustration
  1. $1/2$
  2. $\sqrt2/2$
  3. $\sqrt3/3$
  4. $1+\sqrt2-\sqrt3$
  5. $\sqrt{3/2}$