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2004 AMC 10A Question 21

AMC10 · 2004 AMC 10A

Question 21

Two distinct lines pass through the center of three concentric circles of radii $3,$ $2,$ and $1.$ The area of the shaded region in the diagram is $\dfrac{8}{13}$ of the area of the unshaded region. What is the radian measure of the acute angle formed by the two lines? (Note: $\pi$ radians is $180$ degrees.)

Question illustration
  1. $\dfrac{\pi}{8}$
  2. $\dfrac{\pi}{7}$
  3. $\dfrac{\pi}{6}$
  4. $\dfrac{\pi}{5}$
  5. $\dfrac{\pi}{4}$