Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • In Figure, tangents PQ and PR are drawn to a circle such that angleRPQ = 30degree. A chord RS is drawn parallel to the tangent PQ. Find the angleRQS.

In Figure, tangents PQ and PR are drawn to a circle such that \angleRPQ = 30^{\circ}. A chord RS is drawn parallel to the tangent PQ. Find the \angleRQS.

Answers (1)

best_answer

In the given figure PQ and PR are two tangents drawn from an external point P.
 PQ = PR      [\mathbb{Q} lengths of tangents drawn from an external point to a circle are equal]
\Rightarrow \angle PQR=\angle QRP  

[  angels opposite to equal sides are equal]
  In \bigtriangleupPQR
\angle PQR+\angle QRP+\angle RPQ= 180^{\circ}
                              [  sum of angels of a triangle is 180°]
\angle PQR+\angle PQR+\angle RPQ= 180^{\circ}
\left [ \angle PQR= \angle QRP \right ]
2\angle PQR+30^{\circ}= 180^{\circ}
\angle PQR= \frac{180^{\circ}-30^{\circ}}{2}
\angle PQR= \frac{150^{\circ}}{2}
\angle PQR= 75^{\circ}

SR||OP (Given)

\therefore  \angle SRQ= \angle RQP= 75^{\circ} [Alternate interior angles]      

  Also     \angle PQR= \angle QRS= 75^{\circ}   [Alternate segment angles]    
In \bigtriangleupQRS
\angle Q+\angle R+\angle S= 180^{\circ}
\angle Q+75^{\circ}+75^{\circ}= 180^{\circ}
\angle Q= 180^{\circ}-75^{\circ}-75^{\circ}
\angle Q= 30^{\circ}
\therefore \angle RQS= 30^{\circ}

Posted by

infoexpert27

View full answer

Similar Questions

Latest Question