Corner Shower Rod

I am trying to determine if I have to support the middle of a shower curtain rod. The shower is square and about 40 by 40.

At this distance from the wall at the corner of the rod, I would use a suspended ceiling support. Just pull all the curtain is about to put too much pressure on the wall, and unless you use very heavy anchors, you'll sag or pull on the stick.

Another option is to lose the outer corner of your shower by installing a curved rod, they are becoming more common these days, but you'll still need some kind of support hang from the ceiling. I would go to a superstore for home renovation and talk with them, since you will need to affix the support rod at the ceiling and the need to anchor right for it too. Tell them what type of ceiling you have. I assume that the expansion wing nut anchor bolts is sufficient, you can buy them as small as 1 / 8 inch in diameter and will hold the plasterboard ceiling, especially if you're going to put three or so on the ceiling . It would be useless if you're lucky enough to have some sort of joist, you can screw in the junction of the exact right angle and that would be remotely.
Unless you buy a very specially designed rod, you'll end up with two shower curtains, because they will not because the right angle of the rod sticking down. To avoid this you can wrap the curtain around the corner, but you'd be able to open on each side but not all the way through the set of 40X40 "span.
There are kits that you want to do.
Have you thought about seeing if the distance will accommodate glass doors? doors today at right angles to ensure a good seal where they come together and do not leak water through the town where they meet. More expensive, but nice for the style.

if it sinks? Yeah I put it out and see what happens!