If there are no mounting points on the back, I would get four clips mount at 1, 5, 7, 11 o'clock on the round mirror.

Same deal with the square one, clips on each corner top and bottom

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Try London Glass and Mirror. More on reddit.com

Get a mirror mounting kit, old school style was small brackets and screws that you put above and below the mirror and hold it to the wall. I used one to make a white board using a window pane. More on reddit.com

Depends on the size you want and how comfortable you are with mounting a large mirror. There's something like this: https://www.homedepot.com/p/Dovelina-31-5-in-W-x-47-in-H-Modern-Rectangle-Frameless-Wall-Mounted-Gym-Mirror-Dance-Mirror-JSJ-MR01044/323395012 but it isn't necessary that large and it probably won't provide the straightest reflection for this price (good mirrors of large size are costly). There's also an option to build one yourself from small squares, something like this: https://www.homedepot.com/p/Fab-Glass-and-Mirror-12-in-x-12-in-Frameless-Mirror-Tiles-for-Walls-Pack-of-12-Self-Adhesive-for-Bedroom-Hallway-or-Bathroom-Decor-MT12x12-P12/334267587 The image will be broken up (as these squares won't be perfectly aligned), but they are easy to mount with some 2-sided tape and you can put them in any configuration you want. These are the options that I have found for a large mirror, hopefully somebody suggests better options. More on reddit.com