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2008 AMC 12B Question 8

AMC12 · 2008 AMC 12B

Question 8

Points $B$ and $C$ lie on $\overline{AD}.$ The length of $\overline{AB}$ is $4$ times the length of $\overline{BD},$ and the length of $\overline{AC}$ is $9$ times the length of $\overline{CD}.$ The length of $\overline{BC}$ is what fraction of the length of $\overline{AD}?$
  1. $\dfrac{1}{36}$
  2. $\dfrac{1}{13}$
  3. $\dfrac{1}{10}$
  4. $\dfrac{5}{36}$
  5. $\dfrac{1}{5}$