+743 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 $AF = 1$ and $DF = 2$, then what is $BD$?
+129895 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 $AF = 1$ and $DF = 2$, then what is $BD$?
C
E EF ll CD ED ll BC
A 1 F 2 D B
AE/ AF = AC / AD AE / AD = AC /AB
AE / 1 = AC / 3 AE / 3 = 3AE / AB
3AE = AC 3AE/ AE = AB / 3
3 = AB /3
AB = 9
So.....BD = AB - AD = 9 - 3 = 6
