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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 $$\angle BAC+\angle OBC=$$ ___________.
725953_61de6aa4809b49928703e71eef49b19c.png


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