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If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C and D are concyclic.
Since, ∠BAC = 45° and ∠BDC = 45°
As we know, angles in the same segment of a circle are equal. Hence, A, B, C and D are concyclic.