Question
Write True or False and justify your answer in the following:
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.

Answer

True.

Solution:

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.

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