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Question

BC is chord of a circle with centre O. A is a point on major arc BC. Find the total measure of BAC and OBC.




A

100

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B

90

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C

120

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D

150

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Solution

The correct option is B

90


In ΔOBC, OB = OC (radius)
OBC=OCB=y
Now, z+y+y=180 [Sum of angles of a triangle is 180circ]
z=1802y .... (1)
Also, BOC=2BAC [The angle subtended by an arc at the center is double the angle subtended by it any part of the major arc]
z=2x .... (2)
From (1) and (2),
2x+2y=180x+y=90
BAC+OBC=90


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