In the figure given below, O is the centre of the circle. If $$\angle OBC = 37^\circ$$, the $$\angle BAC$$ is equal to

In the circle, OB=OC (radii), => $$\angle OBC=\angle OCB=37^\circ$$

In $$\triangle$$ OBC, using angle sum property

=> $$\angle BOC+\angle OBC+\angle OCB=180^\circ$$

=> $$\angle BOC+37^\circ+37^\circ=180^\circ$$

=> $$\angle BOC=180^\circ-74^\circ=106^\circ$$

Now, angle subtended by an arc at the centre is double the angle subtended by it at any point on the circle.

=> $$\angle BOC=2\times\angle BAC$$

=> $$\angle BAC=\frac{106^\circ}{2}=53^\circ$$

=> Ans - (C)