(Bicycle) chain is slung over two blocks.
Given: r1, r2, x2, y2 (x1=y1=0) and L.
Find: a form of the chain.
If r1 and r2 -> 0 (or L -> infinity) we have this problem - see here.
Your two pictures assume that one side (either the top or the bottom) is taunt--a straight tangent. But bike sprockets can introduce torque (see your picture in the first post. You can have any intermediate configuration between your two extremes. There's another variable--sprocket torque.