In the figure, O is the centre of a circle,PQL and PRM are the tangents at the points Q and R respectively and Sis a point on the circle such that `angle SQL =50^@ and angle SRM = 60^@`. Then , `angle QSR` is equal to

Options

A. `40^(@)`
B. `50^(@)`
C. `60^(@)`
D. `70^(@)`

Explanation

Since `PQL` is a tangent and `OQ` is a radius, so `/_OQL=90^(@)`
`:./_OQS=90^(@)-50^(@)=40^(@)`
Now, `OQ=OSimplies/_OSQ=/_OQS=40^(@)`
Similarly, `/_ORS=90^(@)-60^(@)=30^(@)`
And, `OR=OSimplies/_OSR=/_ORS=30^(@)`
`:./_QSR=/_OSQ+/_OSR=40^(@)+30^(@)=70^(@)`.