The manufacturer of padlocks of the brand ``K'' wishes to print a logo for his company. This logo has the shape of a stylized capital letter K, inscribed in a square ABCD, with side length one unit of length, and respecting the following conditions C1 and C2:

\begin{itemize}
  \item Condition C1: the letter K must consist of three lines:
  \item one of the lines is the segment $[AD]$;
  \item a second line has endpoints at point A and a point E on segment $[DC]$;
  \item the third line has endpoint at point B and a point G located on the second line.
  \item Condition C2: the area of each of the three surfaces delimited by the three lines drawn in the square must be between 0.3 and 0.4, with the unit of area being that of the square. These areas are denoted $r$, $s$, $t$.
\end{itemize}

We place ourselves in the orthonormal coordinate system $(A; \overrightarrow{AB}, \overrightarrow{AD})$.

\textbf{Part A: study of Proposal A}

In this proposal, the three lines are segments and the three areas are equal: $r = s = t = \frac{1}{3}$. Determine the coordinates of points E and G.