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2018 AMC 8 Question 20

AMC8 · 2018 AMC 8

Question 20

In $\triangle ABC,$ a point $E$ is on $\overline{AB}$ with $AE=1$ and $EB=2.$ Point $D$ is on $\overline{AC}$ so that $\overline{DE} \parallel \overline{BC}$ and point $F$ is on $\overline{BC}$ so that $\overline{EF} \parallel \overline{AC}.$ What is the ratio of the area of $CDEF$ to the area of $\triangle ABC?$

Question illustration
  1. $ \dfrac{4}{9} $
  2. $ \dfrac{1}{2} $
  3. $ \dfrac{5}{9} $
  4. $ \dfrac{3}{5} $
  5. $ \dfrac{2}{3} $