MathematicsState true or false.If A, B, C, and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.

State true or false.


If A, B, C, and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.


  1. A
    True
  2. B
      False 

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    Solution:

    Since we know if points lie on the common chord of the circle, then it is concyclic.
    We have ∠BAC = 45° and ∠BDC = 45°.
    From the above we can see that all points are lying on the circumference of the circle connecting through the same chord BC.
    We also know that the angle made by chord at circle are equal in measure,
    So, angles are equal, which means four points A, B, C and D are concyclic.
    Hence, the statement is true and option 1 is correct.
     
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