Equilibrium Question

[ek]

This question looks really simple, but I'm having surprising difficulty with it.

A hemisperical sign 1 metre in diameter and of uniform mass density is supported by two ropes, as shown in the diagram. What fraction of the sign's weight is supported by each rope?

I am having trouble conceptualizing the question. What is the concept here, and how do I apply what I know in order to figure this out?

[arildno]

1) The sum of the rope tensions must obviously equal mg (the weight of the sign).
This is necessary in order to have TRANSLATIONAL equilibrium of forces.
2) However, we must also have ROTATIONAL equilibrium.
Condition 2), properly framed, will give you the second equation in the two unknowns (the other being condition 1)).