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2009 AMC 10A Question 6

AMC10 · 2009 AMC 10A

Question 6

A circle of radius $2$ is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle’s area is shaded?

Question illustration
  1. $\dfrac{1}{2}$
  2. $\dfrac{\pi}{6}$
  3. $\dfrac{2}{\pi}$
  4. $\dfrac{2}{3}$
  5. $\dfrac{3}{\pi}$