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Question -

In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.



Answer -

It is given that, AB and CD are diameter with center O and  
 
We have to find   
Construction: Join the point A and D to form line AD
Clearly arc AD subtends   at B and   at the centre.
Therefore,  ∠AOD=2∠ABD=100°∠AOD=2∠ABD=100° …… (1)
Since CD is a straight line then
        
∠DOA+∠AOC=180°        (Linear pair)∠DOA+∠AOC=180°        Linear pair
      
Hence  

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