Question

# In the given figure, O is the centre of the circle. If A is any point on minor arc BC, then $$\angle BAC-\angle OBC=$$ _________.

A
45o
B
135o
C
150o
D
90o

Solution

## The correct option is C $$90^o$$$$\angle BAC$$ and $$\angle BOC$$ are supplementary.$$\therefore \angle BOC+\angle BAC=180^o\dots eqn (1)$$ and $$\angle OBC=\angle OCB\,(\because OB=OC)$$$$\Rightarrow \angle OBC=90^o-\angle BOC$$Putting the above value of $$\angle BOC$$ in equation (1), we get$$\angle 90^o-\angle OBC+\angle BAC=180^o$$$$\therefore \angle BAC-\angle OBC=90^o$$Mathematics

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