Q. 354.3( 3 Votes )

In the given figure, O is the center of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that SQL = 50° and SRM = 60°. Then, QSR = ?


A. 40°

B. 50°

C. 60°

D. 70°

Answer :

As PL and PM are tangents to given circle,


We have,


OR PM and OQ PL


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


So, ORM = OQL = 90°


ORM = ORS + SRM


90° = ORS + 60°


ORS = 30°


And OQL = OQS + SQL


90° = OQS + 50°


OQS = 40°


Now, In SOR


OS = OQ [radii of same circle]


ORS = OSR


[Angles opposite to equal sides are equal]


OSR = 30°


[as ORS = 30°]


Now, In SOR


OS = SQ [radii of same circle]


OQS = OSQ


[Angles opposite to equal sides are equal]


OSQ = 40° [as OQS = 40°]


As,


QSR = OSR + OSQ


QSR = 30° + 40° = 70°

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