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# plz help

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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

#4
+23140
+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:

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

Dec 10, 2018

#1
+700
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Use Ceva's Theorem. Learn here

- PM

#2
+700
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some guy also posted the same question here on this website.

#3
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the questions isn't explain nor answered

NerdyKid  Dec 9, 2018
#5
+103947
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Thanks for that reference, PM....I'm not familiar with this......!!!!!

CPhill  Dec 11, 2018
#4
+23140
+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:

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

heureka Dec 10, 2018