Question

In the diagram, PQR is a tangent at Q to the circle with center O.

Find the value of $x$.

• A. ${25}^o$
• B. ${30}^o$
• C. ${35}^o$
• D. ${40}^o$

Answer 1

Answer: (B)

${30}^o$

$\angle QTS=\angle SQR={50}^0$...(alternate segment theorem)
$\angle TSQ=\angle TQP={70}^0$...(alternate segment theorem)
$\angle OQR={90}^0[OQ\perp PR]$...(radius is perpendicular to chord)
$\angle OQS=90-50={40}^0=\angle OSQ$...(angle opposite to same radius)
$\angle TSO=70-40={30}^0$