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1980 AMC 12 Question 21

AMC12 · 1980 AMC 12

Question 21

In triangle $ABC,$ $\angle CBA=72^\circ,$ $E$ is the midpoint of side $AC,$ and $D$ is a point on side $BC$ such that $2BD=DC;$ $AD$ and $BE$ intersect at $F.$ The ratio of the area of $\triangle BDF$ to the area of quadrilateral $FDCE$ is

Question illustration
  1. $\frac15$
  2. $\frac14$
  3. $\frac13$
  4. $\frac25$
  5. none of these