Reference for Pesachim 201:1

אף ידי קידוש לא יצאו אלא לרב למה ליה לקדושי בביתיה כדי להוציא בניו ובני ביתו

They have not done their duty in respect of kiddush either. Then according to Rab, why he [the Reader] recite kiddush at home? - In order to acquit his children and his household [of their duty].

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