Question

According to the figure shown, which of the following is correct?

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A

B

C

D

Both

Medium
Solution
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Correct option is D)

Refer figure:
Construct: Join points and at such that lies on the circumference.
Join

Thus,    ( angle subtended by a chord at the center is twice the angle at the circumference)
thus,

Also, is a cyclic quadrilateral.  Hence,  (sum of opposite angles of a cyclic quadrilateral is 180 degrees)
 
In ,
                  (radius of circle)
               (angles opposite to equal sides are equal)
Hence,


In
   

   
   
Thus,

Summarizing,


Thus, both options A&C are correct.
Correct choice : D

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