Question

In the figure given below, O is the centre of the circle. If ∠OBC=37° ,the ∠BAC is equal to

• A. 74
• B. 106
• C. 53
• D. 37

Answer 1

Answer: (C)

53

Answer 2

From the figure we know that,

$OB = OC$ (as O is the center of the circle and $OB , OC$ the radii of the circle)

$∠ OBC = ∠ OCB = 37^∘$ (given in the question)

By angle sum property of the triangle,

$∠BOC + ∠OBC + ∠OCB = 180^∘$

$∠BOC + 37^∘ + 37^∘ = 180^∘$

$∠ BOC = 180^∘ − 74^∘ = 106^∘$

As we know that angle subtended by an arc at the center is double the angle subtended by it at any point on the circle.

$∠ BOC = 2 × ∠ BAC$

$∠BAC = \frac{106}{2} = 53^∘$

The correct option is (C): 53