In this case it has to do with "ring" being used as "create a border around" or "surround". In this case we use "ringed" instead of "rung": "Dark circles ringed his eyes. "
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The answer would be rung or rang, ringed would only be used for somthing like
example: the fire was ringed around the base of the tree, or
example: the bell rang for school time.
But there are also there are two ways to put it. I think that the question is asking for ringed as in the first example.
Ringed couldn't be used instead of rung or rang.
For words like ro