Meaning of “at the risk of doing sth” in the English Dictionary

british dictionary

"at the risk of doing sth" in British English

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at the risk of doing sth

used before you say something that may seem offensive or stupid:

At the risk of seeming rude, I'm afraid I have to leave now.
At the risk of sounding stupid, how do I send this email?

(Definition of “at the risk of doing sth” from the Cambridge Advanced Learner’s Dictionary & Thesaurus © Cambridge University Press)