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IMAS 2022–2023 Junior Division — First Round Question 15

IMAS · IMAS 2022–2023 Junior Division — First Round

Question 15

The diagram below shows a head of a cartoon character which is represented by a big circle, with its eyes being two circles of radii 1 cm. The two smaller circles are touching at the centre of the big circle and they are also tangent to the big circle. The shaded region represents its hat, for which the horizontal line is tangent to the smaller circles, as shown in the diagram below.

Question illustration

What is the area, in $\text{cm}^2$, of the shaded region?
  1. $\frac43\pi-\sqrt3$
  2. $\frac43\pi$
  3. $\frac23\pi-\sqrt3$
  4. $\frac23\pi$
  5. $\pi-\sqrt3$