The correct answer is: the.
The article “the” is used before a specific noun. In this case, the noun is “library”. The speaker is referring to a specific library, not just any library.
The article “a” is used before an indefinite noun. In this case, the noun is “library”. The speaker is not referring to a specific library, but to any library.
The article “an” is used before a singular noun that begins with a vowel sound. In this case, the noun is “library”. The word “library” does not begin with a vowel sound, so the article “an” is not correct.
The article “none” is used to refer to no one or nothing. In this case, the speaker is not referring to no library or nothing, so the article “none” is not correct.