P$4.$ The T$-$shaped assembly AED shown in the figure is supported by a pin at A and a cable at $E.$ Neglect the weight of the assembly and the friction in the system.

a$)$ Draw the free$-$body diagram of the assembly.

b$)$ Write the three scalar equilibrium equations $F_x=0,F_y=0,$ and $M_A=0.($Do not solve the equations in this part!$).$

c$)$ By solving the equations obtained in part $($b$),$ determine the support reactions at A and the tension in the cable.

d$)$ By drawing the free$-$body diagram of the right segment of the assembly after sectioning$,$ determine the normal force, shear force, and bending moment acting at $C.$

Note: In solving the problem, take the magnitudes of the force and the couple moment shown in the figure as

$F=153N$

$M=420Nm$