plz help

As shown in the diagram Line AD, Line BE  and Line CF are concurrent.

We know that CD=CE=BF=4 and BD=AF=6. 

What is AE?

Ceva's Theorem:

$\begin{array}{|rcll|} \hline \dfrac{AF}{BF}\cdot\dfrac{BD}{CD}\cdot\dfrac{CE}{AE} &=& 1 \\ \\ \dfrac{6}{4}\cdot\dfrac{6}{4}\cdot\dfrac{4}{AE} &=& 1 \\ \\ \dfrac{36}{4AE} &=& 1 \\ \\ AE&=& \dfrac{36}{4} \\ \\ \mathbf{AE}&\mathbf{=}& \mathbf{9} \\ \hline \end{array}$

Use Ceva's Theorem. Learn here. 

  - PM