+72 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?
+26367 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:
\(\begin{array}{|rcll|} \hline \dfrac{AF}{BF}\cdot\dfrac{BD}{CD}\cdot\dfrac{CE}{AE} &=& 1 \\ \\ \dfrac{6}{4}\cdot\dfrac{6}{4}\cdot\dfrac{4}{AE} &=& 1 \\ \\ \dfrac{36}{4AE} &=& 1 \\ \\ AE&=& \dfrac{36}{4} \\ \\ \mathbf{AE}&\mathbf{=}& \mathbf{9} \\ \hline \end{array}\)
+26367 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:
\(\begin{array}{|rcll|} \hline \dfrac{AF}{BF}\cdot\dfrac{BD}{CD}\cdot\dfrac{CE}{AE} &=& 1 \\ \\ \dfrac{6}{4}\cdot\dfrac{6}{4}\cdot\dfrac{4}{AE} &=& 1 \\ \\ \dfrac{36}{4AE} &=& 1 \\ \\ AE&=& \dfrac{36}{4} \\ \\ \mathbf{AE}&\mathbf{=}& \mathbf{9} \\ \hline \end{array}\)
