Patching cement board ceiling in kitchen


I've been helping some friends by doing a few drywall patches for them after they had some plumbing work done, only to discover the hole cut in their kitchen ceiling seems to be in cement board, not drywall.
It's about 10" x 5", and it's not on a stud. The ceiling also has the swirl-pattern, popcorn-texture plaster.
Now, I don't know if cement board is common in kitchen ceilings. I've never come across it before, but I can understand why it makes sense to have fire resistance there. I don't think it's required in Massachusetts, though I've never done a new kitchen ceiling.
What's the best way to go about patching this? Should I cut back to a stud and put in a new piece? Is there a practical way to put a piece in without cutting a lot more out? (I'm a little worried about cutting straight edges in it.) Can it be patched with some wet- patching substance?
I haven't had a chance to go shopping to see what's available yet, but I figured I'd ask ahead of time so I'd have a little more background tomorrow when I do.
The ridiculous thing is that the hole accomplished nothing more than telling the plumber he needed to cut a hole through the behind-the-tub (much more easily repairable) drywall instead.
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It occurred to me after I posted this that the real reason for the concrete board is probably the water above it, not the fire below it, which makes doing this right all the more important.
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Pete from Boston wrote:

Easiest way would be to patch it with a piece of drywall..
1. Insert a piece of ply or 1x2 to bridge the hole. Put some glue on parts that touch the drywall or screw to same.
2. Rough cut a piece of drywall or cement board that will fit in hole
3. Screw #2 to #1
4. Use drywall joint compound or plaster to fill gaps between hole and patch
5. Sand smooth
I'll leave it to you to replicate the ceiling texture.
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dadiOH
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Is it ok to put drywall in under the tub plumbing?
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Pete from Boston wrote:

If the tub leaks the water is going to go *somewhere* regardless of the ceiling material. If using drywall worries you, use a patch cut from cement board.
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dadiOH
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The only thing the ceement board will do is slightly slow down the disintegration of the ceiling if there is a tub leak.
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Cut a piece of strapping about 15 inches long or so and screw it to the cement board while holding it FIRMLY against the BACK of the cement board..Screw in a drywall patch and tape it.....Now you can practice making your swirls or texture on a piece of scrap drywall untill you get it "close" , then do it to the patch....HTH....If you need a help mixing you texture mix , just ask.....
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