A) \[{{170}^{o}}\]
B) \[{{70}^{o}}\]
C) \[{{150}^{o}}\]
D) None of these
Correct Answer: A
Solution :
Given, \[\angle BAO={{50}^{o}},\angle BCO={{35}^{o}}\] ?(i) Now, OA = OB (radii of circle) \[\Rightarrow \]\[\angle BAO=\angle OBA\] (Angles opposite to equal sides are equal) \[\Rightarrow \]\[\angle OBA={{50}^{o}}\] [From (i)] Similarly, \[OB=OC\Rightarrow \angle BCO=\angle OBC\] \[\Rightarrow \] \[\angle OBC={{35}^{o}}\] [From (i)] Now, \[\angle ABC=\angle OBA+\angle OBC={{50}^{o}}+{{35}^{o}}={{85}^{o}}\] \[\therefore \]\[\angle AOC=2\angle ABC=2({{85}^{o}})={{170}^{o}}\]
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