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SASMO 2022 Grade 9 Question 10

SASMO · SASMO 2022 Grade 9

Question 10

In the diagram, square $ABCD$ is inscribed in a circle. Its diagonals meet at $O$. Points $E,F,G,H$ are the midpoints of $AO,BO,CO,DO$, respectively. What fraction of the circle’s area is shaded?

Interpretation: The shaded region is inside ABCD and outside EFGH. The four inner vertices are the named midpoints.

Question illustration
  1. $\dfrac1{2\pi}$
  2. $\dfrac3{2\pi}$
  3. $\dfrac1{4\pi}$
  4. $\dfrac3{4\pi}$
  5. None of the above