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1965 AMC 12 Question 37

AMC12 · 1965 AMC 12

Question 37

Point $E$ is selected on side $AB$ of triangle $ABC$ in such a way that $AE:EB=1:3,$ and point $D$ is selected on side $BC$ so that $CD:DB=1:2.$ The point of intersection of $AD$ and $CE$ is $F.$ Then

$$
\frac{EF}{FC}+\frac{AF}{FD}
$$

is:

Question illustration
  1. $\dfrac45$
  2. $\dfrac54$
  3. $\dfrac32$
  4. $2$
  5. $\dfrac52$