Question
If $A, B, C$ and $D$ are four points such that $\angle\text{BAC}=45^\circ$ and $\angle\text{BDC}=45^\circ,$ then $A, B, C, D$ are concyclic.
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Answer
Since, $\angle\text{BAC}=45^\circ$ and $\angle\text{BDC}=45^\circ$
As we know, angles in the same segment of a circle are equal. Hence, $A, B, C$ and $D$ are concyclic.
As we know, angles in the same segment of a circle are equal. Hence, $A, B, C$ and $D$ are concyclic.
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