Question

In the figure, O is the centre of the circle. If $\angle$BAC = 52${}^{\circ }$, then $\angle$OCB in degree is equal to-

• A. 52
• B. 104
• C. 38
• D. 76

Answer 1

The correct option is C

38

$\angle$BOC = 2($\angle$​BAC) = 104${}^{\circ }$

[The angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle.]

OC = OB [radii of the same circle]

$\angle$​OCB = $\angle$​OBC [angles opposite to the equal sides of a triangle]

In $\Delta$​OBC ,

$\angle$​OCB + $\angle$​OBC + $\angle$BOC = 180${}^{\circ }$ [Angle sum property]

2$\angle$​OCB = 76${}^{\circ }$

$\angle$​OCB = 38${}^{\circ }$