Question

In Fig.2, PQ and PR are two tangents to a circle with centre O. If $\angle QPR={46}^{\circ }$, then $\angle QOR$ equals :

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Given : $\angle QPR={46}^{\circ }$
PQ and PR are tangents.
Therefore, the radius drawn to these tangents will be perpendicular to the tangents.
So, we have $OQ\perp PQ$ and $OR\perp RP$.
$\Rightarrow \angle OQP=\angle ORP={90}^{\circ }$
So, in quadrilateral PQOR, we have
$\angle OQP+\angle QPR+\angle PRO+\angle ROQ={360}^{\circ }$
$\Rightarrow {90}^{\circ }+{46}^{\circ }+{90}^{\circ }+\angle ROQ={360}^{\circ }$
$\Rightarrow \angle ROQ={360}^{\circ }-{226}^{\circ }={134}^{\circ }$
Hence, the correct option is B.