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

The Correct Option is C

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