How can you determine the forces in equilibrium without using calculus?

[quantum_enhan]

Homework Statement

The Attempt at a Solution

I'm not entirely sure how to go about this question, and what to do with the maximum force that each cord can withstand. I tried setting up an equation, then taking a derivative to solve it for the maximum, but I bet there is an easier way, since the derivative got quite messy... Suggestions?

 

[Redbelly98]

Nothing moves, so what do you know about the net force acting on each ring at A, B and C?

p.s. By the way, calculus is not needed here.