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IMAS 2023–2024 Junior Division — First Round Question 7

IMAS · IMAS 2023–2024 Junior Division — First Round

Question 7

In the diagram below, two circles, each of radius 6 cm, are there such that their centres lie on the circumference of the other. What is the area, in $\mathrm{cm}^2$, of the region common to both circles?

Question illustration
  1. $12\pi-9\sqrt3$
  2. $24\pi-18\sqrt3$
  3. $24\pi-9\sqrt3$
  4. $4\pi-\sqrt3$
  5. $24\pi-3\sqrt3$