Question

In the given figure, O is the centre of the circle and $\angle BAC=n^{\circ }$ $\angle OCB=m^{\circ }$

• A. $m+n=$ ${90}^{\circ }$
• B. $m+n=$ ${180}^{\circ }$
• C. $m+n=$ ${120}^{\circ }$
• D. $m+n=$ ${150}^{\circ }$

Answer 1

The correct option is A $m+n=$ ${90}^{\circ }$

$\angle BOC=2\angle BAC$, the angle formed at the centre is twice the angle formed at the circumference.
Therefore, $\angle BOC=2n$
$\angle OCB=m$
Since, OB = OC = radius of the circle = m
Thus, in $\Delta$ OBC,
$\angle OCB+\angle OBC+\angle BOC={180}^{\circ }$
$2m+2n=180$
$\Rightarrow m+n=90$