Question

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

• A. 52
• B. 104
• C. 38
• D. 76

Answer 1

The correct option is C

38

Since, he 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,

So,

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

$OC=OB$ [radii of the same circle]

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

In $△OBC,$

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

$\Rightarrow 2\angle OCB=180-104={76}^{\circ }$

$\Rightarrow \angle OCB={38}^{\circ }$