Sag-Span Ratio

What is the minimum length $L_{min}$ of a flexible cable $AC$ of a uniform weight per unit length $w$ which can hang in equilibrium as shown below:

Neglect friction and the dimensions of the pulley $B$ . Assume the horizontal force in the rope at the lowermost position of sag be $H$ . Let the sag-span ratio be $a$ $\frac{f}{l}=a$ and $\frac{H}{wl}=b$ and $\frac{L_{min}}{l}=c$

Evaluate $a+b+c$ .