$4\mathrm{.}117$

A $100-kg$ uniform rectangular plate is supported in the position shown by hinges A and $B$ and by cable DCE that passes over a frictionless hook at $C.$ Assuming that the tension is the same in both parts of the cable, determine $($a$)$ the tension in the cable, $(b)$ the reactions at A and $B.$ Assume that the hinge at $B$ does not exert any axial thrust.

Fig. P$4\mathrm{.}117$