3.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-06_645_684_260_639}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

The uniform lamina $A B C D$ is a square of side $6 a$. The template $T$, shown shaded in Figure 1, is formed by removing the right-angled triangle $E F G$ and the circle, centre $H$ and radius $a$, from the square lamina.

Triangle $E F G$ has $E F = E G = 4 a$, with $E F$ parallel to $A B$ and $E G$ parallel to $A D$. The distance between $A B$ and $E F$ is $a$ and the distance between $A D$ and $E G$ is $a$.

The point $H$ lies on $A C$ and the distance of $H$ from $B C$ is $2 a$.
\begin{enumerate}[label=(\alph*)]
\item Show that the centre of mass of $T$ is a distance $\frac { 4 ( 67 - 3 \pi ) } { 3 ( 28 - \pi ) } a$ from $A D$.

The template $T$ is suspended from the ceiling by two light inextensible vertical strings. One string is attached to $T$ at $A$ and the other string is attached to $T$ at $B$ so that $T$ hangs in equilibrium with $A B$ horizontal.

The weight of $T$ is $W$. The tension in the string attached to $T$ at $B$ is $k W$, where $k$ is a constant.
\item Find the value of $k$, giving your answer to 2 decimal places.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2021 Q3 [8]}}