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Australian AMC 2019 - Senior Question 24

AMC AUSTRALIA · Australian AMC 2019 - Senior

Question 24

A circle $C$ and a regular hexagon $H$ have equal area. A regular hexagon $H^{\prime}$ is inscribed in $C$, and a circle $C^{\prime}$ is inscribed in $H$.
What is the ratio of the area of $H^{\prime}$ to the area of $C^{\prime}$?

Question illustration
  1. 1 : 1
  2. $3:\pi$
  3. $9:\pi^2$
  4. 3 : 4
  5. $3\sqrt3:2\pi$