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I have had good luck glueing plastics with an adhesive called Bondic.
It cures using a supplied UV light
It hase held things attached that neither 2 part epoxy or CA glue would.
The shelves on the doors on our nocold kept falling off. I used Gorilla epoxy to keep them in place. Been holding pretty good for about 3 weeks now. I put a dab on each top corner and a bead across the bottom. That may work well on the broken piece.