If a checked exception is thrown in the catch block, it MUST also be declared. If a checked exception is thrown inside a method, it must EITHER be caught in a try catch block OR declared. But what happens if we both declare AND catch a checked exception(thrown in a try block and caught in a matching catch block)? Does it generate a compilation error? Should the methods calling the present method declare/catch the exception thrown in the present method?
The best way to verify this is to write some code and experiment with it. But note that declaring an exception simply indicates that an exception might be thrown -- there is no requirement to actually throw one. So if it ends up being caught...
"We're kind of on the level of crossword puzzle writers... And no one ever goes to them and gives them an award." ~Joe Strummer sscce.org
But be aware that for checked exceptions, the compiler will pay attention to whether they are caught or not (that's what the "checked " means after all). If you declare a checked exception, and the compiler can tell that the exception is definitely caught and not rethrown, then the compiler will complain that you've declared a checked exception which is not thrown.
Note that for unchecked exceptions, none of this applies. You can catch them or declare them, both or neither. You're on your own; the compiler doesn't care.