A (weightless) cable of length [math]r[/math] is attached to the ceiling at point [math]A[/math]. The other end of the cable is attached to a pulley (point [math]C[/math]). The end of another cable of length [math]l[/math] is attached to the ceiling at point [math]B[/math], where [math]|AB|=d[/math] ([math]d>r[/math]). At the other end of the second cable (point [math]D[/math]) is attached a weigh. This second cable passes over the pulley (so [math]|BC|+|CD|=l[/math]), and the whole system is allowed to adjust itself to reach a state of stationary equilibrium. The question is: How far below the ceiling is the final position of the weight?
Drag the point [math]C[/math] until you find the point of equilibrium. This occurs when [math]D[/math] is as low as possible.