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Australian AMC 2009 - Senior Question 24

AMC AUSTRALIA · Australian AMC 2009 - Senior

Question 24

Four circles of radius 1 cm are drawn with their centres at the four vertices of a square with side length 1 cm. The area, in square centimetres, of the region overlapped by all four circles is
  1. $2\sqrt3-\pi$
  2. $\pi-\sqrt2$
  3. $1+\frac\pi3-\sqrt3$
  4. $\pi-2\sqrt2$
  5. $\frac{\pi-3-\sqrt3}2$