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Question

In the given figure, O is the centre of the circle. Which of the following option is correct?



 
  1. x+y=z
  2. y=z
  3. x+2y=z
  4. 2x=z


Solution

The correct option is A x+y=z
Since, the angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle
EBF=12EOF=12z
ABC=18012z  (Sum of all angles on a line is 180)(i)
Similarly, EDF=12EOF=12z
ADC=18012z (Sum of all angles on a line is 180)(ii)    
Now, in quadrilateral ABCD
ABC+BCD+CDA+BAD=360 (Angle sum property of a quadrilateral)(iii)  
18012z+y+18012z+x=360
x+y=z

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