A prayer offered away from the qibla without taharri must be repeated

Question

A certain person prayed facing north, being certain that the west was in that very direction, and so he did not perform taharri (determining the direction by reasoned judgement), since taharri is needed only when one knows that the qibla is in doubt. After finishing [the prayer] he learned of his mistake. Is it now wajib for him to repeat that prayer or not?

Answer

Such a prayer must be repeated — just as when someone performs wudu' believing the water to be pure [and it turns out not to be], or the garment was impure: repeating (i'ada) such a prayer is obligatory.

Source: Fatawa Mahmudiyya

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