Problem source

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\noindent \begin{center}
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.5pt,arrowsize=3pt 2,arrowinset=0.25} \begin{pspicture*}(-2.4,-1.16)(12.46,5.7) \psline(0,0)(6,4) \psline(10,0)(5,5) \rput[tl](5.08,5.53){$D$} \rput[tl](5.31,4.3){$B$} \rput[tl](3.39,2.99){$2l$} \pscustom[fillcolor=black,fillstyle=solid,opacity=0]{\parametricplot{0.0}{0.5880026035475675}{1.23*cos(t)+0|1.23*sin(t)+0}\lineto(0,0)\closepath} \rput[tl](0.67,0.39){$\alpha$} \pscustom[fillcolor=black,fillstyle=solid,opacity=0]{\parametricplot{2.356194490192345}{3.141592653589793}{1.23*cos(t)+10|1.23*sin(t)+0}\lineto(10,0)\closepath} \rput[tl](9.09,0.56){$\beta$} \psline{->}(8,2)(8,1.3) \rput[tl](7.64,1.31){$Mg$} \rput[tl](9.17,1.38){$x$} \rput[tl](7.27,3.32){$x$} \rput[tl](-0.29,-0.18){$A$} \rput[tl](10.15,-0.2){$C$} \psline(-2,0)(12,0) \end{pspicture*}
\par\end{center}

The above diagram illustrates a makeshift stepladder, made from two
equal light planks $AB$ and $CD$, each of length $2l$. The plank
$AB$ is smoothly hinged to the ground at $A$ and makes an angle
of $\alpha$ with the horizontal. The other plank $CD$ has its bottom
end $C$ resting on the same horizontal ground and makes an angle
$\beta$ with the horizontal. It is pivoted smoothly to $B$ at a
point distance $2x$ from $C$. The coefficient of friction between
$CD$ and the ground is $\mu.$ A painter of mass $M$ stands on $CD$,
half between $C$ and $B$. Show that, for equilibrium to be possible,
\[
\mu\geqslant\frac{\cot\alpha\cot\beta}{2\cot\alpha+\cot\beta}.
\]
Suppose now that $B$ coincides with $D$. Show that, as $\alpha$
varies, the maximum distance from $A$ at which the painter will be
standing is 
\[
l\sqrt{\frac{1+81\mu^{2}}{1+9\mu^{2}}}.
\]