\begin{TP}[Jardins royaux][\tice]

\parpic[r]{
\begin{tikzpicture}[general, scale=0.22]
\clip(-19.43,-7) rectangle (20.88,4.68);
\draw[fill=A2] (7.83,-1.21) -- (7.3,-0.27) -- (6.35,-0.79) -- (6.88,-1.74) -- cycle; 
\draw[dashed] (2.1,3.2)--(2.1,-1.74)-- (6.88,-1.74);
%\draw [color=zzttqq] (2.02,-1.66)-- (6.88,-1.74);
%\draw [color=zzttqq] (2.1,3.2)-- (2.02,-1.66);
\draw (-16.12,-1.36)-- (2.1,3.2);
\draw (2.1,3.2)-- (20.16,-1.96);
\draw (20.16,-1.96)-- (1.94,-6.52);
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\draw (-5.01,-3.05) -- (-5.23,-2.65);
\draw (-2.84,-1.58)-- (-0.48,-5.83);
\draw (-1.55,-3.44) -- (-1.95,-3.66);
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\draw (11.13,0.62)-- (6.88,-1.74);
\draw (9.27,-0.67) -- (9.05,-0.27);
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\draw (8.96,-0.85) -- (8.74,-0.45);
\draw (4.52,2.51)-- (6.88,-1.74);
\draw (5.81,0.65) -- (5.41,0.43);
\draw (5.9,0.5) -- (5.5,0.27);
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\draw (1,-1.76) node {$A$};
\draw (7.08,-2.75) node {$B$};
\draw (2.48,3.9) node {$D$};
\draw (4.94,3.25) node {$N$};
\draw (11.53,1.4) node {$V$};
\end{tikzpicture}}
Pedro est jardinier dans une quinta à Sintra au Portugal. 
Il souhaite réaliser un parterre de fleurs suivant le motif schématisé ci\nobreakdash-contre. 
Les segments codés de même longueur mesureraient tous \um{2}, ainsi que $[AB]$ et $[AD]$. 
Il souhaite que l'angle $\widehat{VBN}$ soit droit, et il veut s'assurer que les points $D$, $N$ et $V$ soient alignés. 

 

\begin{enumerate}
 \item {\bfseries Reproduction d'une partie de cette figure} 
 \begin{enumerate}
  \item Tracer un triangle $ABN$ équilatéral.
  \item Placer $D$, du même côté de $(AB)$ que $N$, tel que $ABD$ soit isocèle rectangle en $A$.
  \item Placer $V$, du même côté de $(AB)$ que $N$, tel que $VBN$ soit isocèle rectangle en $B$.
%  \item La droite $(DN)$ coupe $(AB)$ en $M$. Terminer la figure en traçant le triangle $ADM$ 
 \end{enumerate}
\item {\bfseries Démonstration}
\begin{enumerate}
\item Déterminer les coordonnées de $D$, $N$ et $V$ dans le repère $(A; B,D)$.
\item Vérifier que les trois points sont alignés en utilisant un logiciel de calcul formel pour effectuer les simplifications d'écriture. 
\end{enumerate}


\end{enumerate}
\end{TP}