Question

In the given figure, O is the centre of the circle and $\angle OBC={50}^o$. Then $\angle BAC$ is

• A. $\angle BAC={80}^o$
• B. $\angle BAC={40}^o$
• C. $\angle BAC={60}^o$
• D. $\angle BAC={30}^o$

Answer 1

The correct option is B $\angle BAC={40}^o$

In $△OBC$

$\Rightarrow$ $\angle OBC=\angle OCB={50}^o$ [ $OB$ and $OC$ radii of circle so base angle will be equal ]

$\Rightarrow$ $\angle OBC+\angle OCB+\angle BOC={180}^o$

$\Rightarrow$ ${50}^o+{50}^o+\angle BOC={180}^o$

$\Rightarrow$ $\angle BOC={180}^o-{100}^o$

$\Rightarrow$ $\angle BOC={80}^o$

Here, $\angle BAC$ angel $\angle BOC$ are subtended by same arc $BC$

We know, Angle subtended by an arc at the center is double the angle subtended by it at angle other point on circle.

$\therefore$ $\angle BOC=2\angle BAC$

$\Rightarrow$ ${80}^o=2\angle BAC$

$\therefore$ $\angle BAC={40}^o$