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Question

Mark (✓) against the correct answer in each of the following:
In the given figure, O is the centre of a circle and ∠BAC = 40°. Then, ∠OBC = ?
(a) 40°
(b) 50°
(c) 80°
(d) 20°

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Solution

(b) 50°

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the circumference of the circle.So,BOC=2BACBOC=2×40°=80°Now, BO=OC. So,BOC is an isoceles triangle.In BOC, BOC+OBC+BCO=180° (Angle-sum property)80°+OBC+OBC=180° (OBC=BCO)2OBC=180°-80°2OBC=100°OBC=50°

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