Question
If A, B, C, D are four points such that $\angle\text{BAC}=30^\circ$ and $\angle\text{BDC}=60^\circ$ then D is the centre of the circle through A, B and C.

Answer

False.
Solution: Because, there can be many points D, such that $\angle\text{BDC}=60^\circ$ and each such point cannot be the centre of the circle through A, B and C.

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