Quote, cite, repeat are not close synonyms, though all mean to speak or write again something already said or written by another.
Quote usually implies a use of another’s words, commonly with faithful exactness or an attempt at it, for some special effect like adornment, illustration, close examination.
But sometimes quote is applied to a more general referral to someone as the author or source of information without implication of precise reproduction of an original statement.
Cite is likely to stress the idea of adducing, bringing forward, or mentioning for a particular reason, like substantiation or proof, with or without the idea of uttering another’s words.
Repeat stresses the fact of a saying or writing over again of someone else’s words often with no reference to the source.
Typically it carries none of the implication of formal or dignified reasons for the procedure that attaches to quote and cite .