A) \[90{}^\circ \]
B) \[100{}^\circ \]
C) \[120{}^\circ \]
D) \[150{}^\circ \]
Correct Answer: A
Solution :
Refer the question figure. In \[\Delta OBC,OB=OC\](= radius) \[\Rightarrow \]\[\angle OBC=\angle OCB=y\] Now, \[z+y+y={{180}^{o}}\] \[\Rightarrow \] \[z={{180}^{o}}-2y\] ?..(i) Also, \[\angle BOC=2\angle BAC\] \[\Rightarrow \]\[z=2x\] ?...(ii) From (i) and (ii), \[\Rightarrow \]\[2x+2y={{180}^{o}}\Rightarrow x+y={{90}^{o}}\] \[\therefore \]\[\angle BAC+\angle OBC={{90}^{o}}\]
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