
\begin{minipage}{0.4\linewidth}
\begin{tikzpicture}
%\draw (0,0) -- (0:0.6) arc (0:45:0.6) -- cycle;
\draw (5.121320343559642,0.2828427124746191) -- (4.838477631085023,0.2828427124746192) -- (4.838477631085023,0) -- (5.121320343559642,0) -- cycle; 
\draw (3,0.2828427124746191) -- (2.7171572875253807,0.2828427124746192) -- (2.7171572875253807,0) -- (3,0) -- cycle; 
\draw (0,0)-- (3,0);
\draw(1.45,0.12) -- (1.45,-0.12);
\draw (1.55,0.12) -- (1.55,-0.12);
\draw (3,0)-- (3,3);
\draw(2.88,1.45) -- (3.12,1.45);
\draw (2.88,1.55) -- (3.12,1.55);
\draw (3,3)-- (0,0);
\draw(3,3)-- (5.121320343559642,5.121320343559642);
\draw (3.940452018978107,4.110157646462878) -- (4.11015764646288,3.940452018978107);
\draw (4.01116269709676,4.1808683245815335) -- (4.180868324581533,4.011162697096762);
\draw [dashed] (3,0)-- (5.121320343559642,0);
\draw [dashed] (5.121320343559642,0)-- (5.121320343559642,5.121320343559642);
\draw (5.121320343559642,5.121320343559642)-- (3,0);
\node[below left] at (0,0) {A};
\node[below] at (3,0) {B};
\node[above] at (3,3) {C};
\node[above right] at (5.12,5.12) {D};
\node[below] at (5.121320343559642,0) {H};
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.6\linewidth}
\begin{itemize}
\item $ABC$ est un triangle rectangle isocèle en $B$.
\item On note $AB = a$.
\item Les points $A$, $C$ et $D$ sont alignés.
\item $CD = a$.
\item $H$ est le projeté orthogonal de $D$ sur $(AB)$.
\end{itemize}
\end{minipage}
\begin{enumerate}
\item Montrer que $DA = \big(1+\sqrt2\big)a$.
\item À l'aide du théorème d'Al-Kashi, montrer que $DB = a\sqrt{2+\sqrt2}$.
\item Montrer que $\prodscal{DA}{DB} =a^2 \big(1+\sqrt2\big)\sqrt{2+\sqrt2}\cos\dfrac{\pi}{8}$.
\item À l'aide de la relation de Chasles, montrer que $\prodscal{DA}{DB}=\dfrac{1}{2}a^2\big(1+\sqrt2\big)^2\sqrt2$.
\item En déduire que $\cos\dfrac{\pi}{8}=\dfrac{\sqrt{2+\sqrt2}}{2}$
\end{enumerate}

