 ## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 35 of Multiple Choice Questions (MCQ)

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35
##### 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 = ? 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°

35

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