$ (A) \ 67$ 
$( B) \ 134$
$( C) \ 44$ 
$( D) \ 46$"
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In Fig. 2, PQ and PR are two tangents to a circle with centre O. If $\angle QPR=46^{o}$, then $\angle QOR$ equals:

$ (A) \ 67$ 
$( B) \ 134$
$( C) \ 44$ 
$( D) \ 46$"

Given: PQ and PR are two tangents to a circle with center O. And $\angle QPR=46^{o}$

To do: To find the value of $\angle QOR\ =?$

Solution: $\angle QPR=46^{o}$, PQ and PR are tangents

Therefore, the radius drawn to these tangents will be perpendicular to the tangents So, we have

$OQ\bot PQ$ and $OR\bot RP$ 

$\Rightarrow \angle OQP=\angle ORP=90^{o} \ $

So, In quadrilateral PQRS,

We have $\angle OQP\ +\angle OPR+\angle PRO+\angle ROQ=360^{o}$ 

$\Rightarrow 90^{o} +46^{o} +90^{o} +\angle ROQ=360^{o}$

$\angle ROQ=360^{o} -226^{o} =134^{o}$

Hence, The correct option is $( B)$
 

Updated on: 10-Oct-2022

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