A cylindrical support column at a construction site needs to withstand a compressive axial load of $\backslash (90,000\backslash$mathrm$\{$~N$\}\backslash )$ while also being subjected to a twisting torque of $\backslash (2,500\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash )$ due to equipment vibrations. The column has a diameter of $200$ mm and is firmly anchored at its base. The column is made of a brittle material.

The material properties are as follows:

$-$ Ultimate compressive strength, $\backslash (\backslash$sigma c$=80\backslash$mathrm$\{$MPa$\}\backslash )$

$-$ Ultimate tensile strength, $\backslash (\backslash$sigma $\backslash$mathrm$\{$t$\}=20\backslash$mathrm$\{$MPa$\}\backslash )$

Engineers need to evaluate whether the column will fail under these combined loading conditions using the Mohr's failure criterion for brittle materials.

a$)$ Calculate the principal stresses at the critical point on the surface of the column.

b$)$ Identify the orientation of the principal stresses relative to the column's axis.

c$)$ Determine if the column is safe or will fail under the applied loads using the Mohr's failure criterion.