Determine the smallest force F that must be applied along the rope in order to cause the

Question:

Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has radius r, to fail at the support C. This requires a moment to be developed at C of magnitude M.

Given:
r = 5 ft
M = 80 lb⋅ ft
θ = 60 deg
a = 7 ft
b = 6 ft