Question

# BC is a chord of a circle with centre O. If A is a point on major arc BC as shown in the figure, then $$\angle BAC+\angle OBC=$$ ___________.

A
45o
B
90o
C
180o
D
165o

Solution

## The correct option is B $$90^o$$$$\angle OBC=\angle OCB=\dfrac{1}{2}(180-\angle BOC )$$From the figure, $$\angle BAC=\dfrac{1}{2}\times \angle BOC$$$$\therefore \angle OBC=90^o-\angle BAC\\ \Rightarrow \angle BAC+\angle OBC=90^o$$Mathematics

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