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Australian AMC 2016 - Senior Question 23

AMC AUSTRALIA · Australian AMC 2016 - Senior

Question 23

What is the radius of the largest sphere that will fit inside a hollow square pyramid, all of whose edges are of length 2?
  1. $\sqrt2-1$
  2. $\frac{2-\sqrt2}{2}$
  3. $\frac{\sqrt6-\sqrt2}{2}$
  4. $\frac{\sqrt3}{3}$
  5. $\frac{\sqrt2}{4}$