What the right way to fix this? This is the opening to a chimney, for the vent pipe for a water heater. I needed to enlarge the opening from 3 inch to 4 inch. You can see the round part on the left side.
I was cutting it larger with a hammer drill, and this piece came out (you can see my marking for the new size I need, and the holes I drilled to cut it):
The back side, has some brick and some plaster (and yes, whoever did this before me stuffed it with newspaper, which can still be read, 20 or more years later):
You can see how the broken piece fits in the wall:
Should I glue the piece back in? Is there some kind of flat metal plate I can just put over the entire thing? Ignore the broken piece and just rebuild it with plaster?