iran-konkur 2015 Q127

iran-konkur · Other · konkur-riazi_1394 Not Maths
127- In triangle $ABC$ $\left(AB = \dfrac{2}{3}AC\right)$, $ND$ is a line segment parallel to $AM$ where $AM$ is the median. What is the ratio $\dfrac{AD}{AE}$?
[Figure: Triangle $ABC$ with points $D$, $E$, $M$, $N$ where $B$, $M$, $N$, $C$ are on the base, $A$ is the apex, and $D$, $E$ are on sides $AD$ and $AE$ respectively]
  • [(1)] $\dfrac{4}{9}$
  • [(2)] $\dfrac{5}{9}$
  • [(3)] $\dfrac{2}{3}$
  • [(4)] $\dfrac{4}{5}$

%% Page 24
\textbf{127-} In triangle $ABC$ $\left(AB = \dfrac{2}{3}AC\right)$, $ND$ is a line segment parallel to $AM$ where $AM$ is the median. What is the ratio $\dfrac{AD}{AE}$?

\textit{[Figure: Triangle $ABC$ with points $D$, $E$, $M$, $N$ where $B$, $M$, $N$, $C$ are on the base, $A$ is the apex, and $D$, $E$ are on sides $AD$ and $AE$ respectively]}

\begin{itemize}
\item[(1)] $\dfrac{4}{9}$
\item[(2)] $\dfrac{5}{9}$
\item[(3)] $\dfrac{2}{3}$
\item[(4)] $\dfrac{4}{5}$
\end{itemize}



%% Page 24