Divulge verb - To make known (as information previously kept secret).
Usage example: we tried to make him divulge the name of the winner, but he wouldn't budge
Leak is a synonym for divulge in confess topic. In some cases you can use "Leak" instead a verb "Divulge", when it comes to topics like expose, make known.
Leak verb - Tell anonymously.
Usage example: The news were leaked to the paper
Divulge is a synonym for leak in disclose topic. You can use "Divulge" instead a verb "Leak", if it concerns topics such as seep.
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Google Ngram Viewer shows how "divulge" and "leak" have occurred on timeline