You mentioned 'adhesive tape' and then wondered if 5200 would work. If the bracket and surface you're trying to fasten it to are plastic, another adhesive might work. I'd outline the spot you want the hanger to be and rough the surface up with fine sandpaper. Then test a cement made for plastics on the bracket and the roughed up spot. You want a solvent that actually melts the plastic, creating a 'weld.' Perhaps modeler's plastic glue is all you need.
If the back of the bracket is flat, a stronger double-sided foam tape might also work. 3M makes a variety of different strength adhesives on their foam tape, from temporary to permanent grade.
*Â*Foam Tape