Considered odd, having been eaten by a bear? (9)

I believe the answer is:

ruminated

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'considered odd having been eaten' is the definition.
I can't tell whether this definition defines the answer.

'by a bear?' is the wordplay.
'by' becomes 'rumina' (I can't explain this - if you can you should give a lot more credence to this answer).
'a bear?' becomes 'ted' (teddy bear).
'rumina'+'ted'='RUMINATED'

Can you help me to learn more?

(Another definition for ruminated that I've seen is " Pondered".)

I've seen this clue in The Times.

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