Question

If $AP$ and $AQ$ are the two tangents a circle with centre $O$ so that $\angle POQ={110}^o$ , then $\angle PAQ$ is equal to :

• A. ${60}^o$
• B. ${70}^o$
• C. ${80}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${70}^o$

R.E.F image

$\angle A+\angle P+\angle Q+\angle O=360$

(sum of Angles in a

quadrilateral APOQ)

$\Rightarrow \angle A+{90}^{\circ }+{90}^{\circ }+{110}^{\circ }={360}^{\circ }$

$\Rightarrow \angle A={70}^{\circ }$

$\angle PAQ={70}^{\circ }$ (B)