Question

If AP and AQ are the two tangents to a circle with centre 'O' so that $\angle POQ$ = 120°, then$\angle PAQ$ is equal to ___.

• A. 70$°$
• B. 60$°$
• C. 80$°$
• D. 90$°$

Answer 1

The correct option is B 60$°$

By Theorem- If two tangents AP and AQ are drawn to a circle with centre O from an external point A, then$\angle PAQ=2\angle OPQ=2OQP$
(or) $\angle OPQ=\angle OQP=\frac{1}{2}\times \angle PAQ$.

If we join P and Q then we get a $△$ $POQ$.
$\because$ Sum of angles in a triangle is equal to ${180}^{\circ }$
$\therefore$ $\angle POQ+\angle OPQ+\angle OQP={180}^{\circ }$
on substituting $\angle OPQand\angle OQP$
we get,
$\angle POQ$ + $\frac{1}{2}$$\angle PAQ$ + $\frac{1}{2}$$\angle PAQ$ = ${180}^{\circ }$
Given, $\angle POQ={120}^0$
$\therefore$ ${120}^0+\angle PAQ={180}^0$
$\Rightarrow$ $\angle PAQ={60}^0$