question_answer

In the given figure, O is the centre of the circle. If PA and PB are tangents, then the value of \[\angle AQB\] is               

A) \[{{100}^{o}}\]                   

B)        \[{{80}^{o}}\]                     

C)        \[{{60}^{o}}\]                     

D)        \[{{50}^{o}}\]                     

Correct Answer: D

Solution :

Since PA and PB are tangents. Also, tangent is \[\bot \] r to radius through point of contact,              \[\therefore \]   \[\angle PAO={{90}^{o}}\] and  \[\angle PBO={{90}^{o}}\] in quadriiateral APBO;             \[\angle APB+\angle PAO+\angle PBO+\angle AOB={{360}^{o}}\] \[{{80}^{o}}+{{90}^{o}}+{{90}^{o}}+\angle AOB={{360}^{o}}\] \[\Rightarrow \] \[\angle AOB={{100}^{o}}\] \[\Rightarrow \] \[\angle AQB=\frac{1}{2}\angle AQB=\frac{1}{2}\angle AOB={{50}^{o}}\]