In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 9$ and $DF = 3$, then what is $BD$?
Have you drawn the picture?
If you have then you will see that there are 2 pairs of similar triangles.
You can solve the ratios simultaneously to get your answer. This part is actually very easy.
If you want to interact with me then you are encouraged to do so.
+32 
