Question

$\text{If TP and TQ are two tangents to a circle}\text{with center O such that}\angle POQ={110}^o,\text{then}\angle PTQ\text{will be}$.

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

Answer 1

The correct option is A ${70}^{\circ }$

$\text{Given:}\angle POQ={110}^{\circ }$

TP and TQ are tangents.
A tangent at any point of a circle is perpendicular to the radius at the point of contact.

$\Rightarrow \angle OQT=\angle OPT={90}^{\circ }$

We know that, sum of interior angles of a quadrilateral is 360 degrees.

$\angle TQO+\angle QOP+\angle OPT+\angle PTQ={360}^{\circ }$

${90}^{\circ }+{110}^{\circ }+{90}^{\circ }+\angle PTQ={360}^{\circ }\Rightarrow \angle PTQ={360}^{\circ }–{90}^{\circ }–{90}^{\circ }–{110}^{\circ }\Rightarrow \angle PTQ={70}^{\circ }\therefore \angle PTQ={70}^{\circ }$