Question

In the given figure, if $ TP$ and $ TQ$ are the two tangents to a circle with center $ O$ so that $ \angle POQ = {110}^{\circ }$, then$ \angle PTQ$ is equal to

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

Answer 1

The correct option is B

${70}^{\circ }$

Find the value of $\angle PTQ$

A tangent is perpendicular to the radius at the point of contact

$\therefore TP\perp OP$ and $TQ\perp OQ$

$\therefore \angle TPO=\angle TQO={90}^{\circ }$

By angle sum property of a quadrilateral

$\angle PTQ+\angle TQO+\angle TPO+\angle POQ={360}^{\circ }$

$\Rightarrow$ $\angle PTQ={360}^{\circ }-{110}^{\circ }-{90}^{\circ }-{90}^{\circ }$

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

Hence, $\angle PTQ={70}^{\circ }$, so, option $\left(B\right)$ is the correct answer.