\begin{exercice}On considère un rectangle $ABCD$ du plan.

\begin{center}
\begin{tikzpicture}[general,scale=0.7]
\draw (0,0) rectangle (5,3) ;
   \draw (0,0) node[below]{$A$} ;
   \draw (5,0) node[below]{$B$} ;
   \draw (5,3) node[above]{$C$} ;
   \draw (0,3) node[above]{$D$} ;
  \end{tikzpicture}
\end{center}

Déterminer l'ensemble des points $M$ tels que :
\begin{colenumerate}{2}
    \item $\vv{AD}\cdot \vv{AM}=AD^2$
  \item $\vv{BC}\cdot \vv{AM}=BC^2$
  \item $\vv{AB}\cdot \vv{AM}=\dfrac{AB^2}{2}$
  \item $\vv{AD}\cdot \vv{AM}=\dfrac{AD^2}{2}$
\end{colenumerate}

\end{exercice}
