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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?

 

 Dec 9, 2018

Best Answer 

 #4
avatar+21855 
+11

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:

 

    

 

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

 

 

laugh

 Dec 10, 2018
 #1
avatar+679 
0

Use Ceva's Theorem. Learn here

 

  - PM

 #2
avatar+679 
0

some guy also posted the same question here on this website.

 #3
avatar+72 
+1

the questions isn't explain nor answered

NerdyKid  Dec 9, 2018
 #5
avatar+98102 
0

Thanks for that reference, PM....I'm not familiar with this......!!!!!

 

 

cool cool cool

CPhill  Dec 11, 2018
 #4
avatar+21855 
+11
Best Answer

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:

 

    

 

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

 

 

laugh

heureka Dec 10, 2018

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