Question

If TP and TQ are two tangents to a circle with center O such 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

${70}^{\circ }$

Given that $\angle POQ={110}^{\circ }$
Note that $\angle OQT=\angle OPT={90}^{\circ }$
($\because$ A tangent at any point of a circle is perpendicular to the radius at the point of contact)

Also, $\angle TQO+\angle QOP+\angle OPT+\angle PTQ={360}^{\circ }$($\because$ Sum of interior angles of a quadrilateral is 360 degrees)

$⟹\angle PTQ={360}^{\circ }–{90}^{\circ }–{90}^{\circ }–{110}^{\circ }$

$⟹\angle PTQ={70}^{\circ }$

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