**Tangents PQ and PR are drawn to a circle such that angle RPQ= 30 degreeA chord RS is drawn parallel to tangent PQ.Find angle RQS...??? ANSFAST...**

tangents PQand PR are drawn to a circles such that angles RPQ=30degree a chord RS is drawn parallel to tangents PQ find angle RQS

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rshimpy86... Can u explain this in detail...

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Tangents drawn from an external point to a circle are equal

Hence, PQ = PR

And PQR is an isosceles triangle

ThereforeRQP =QRP

RQP +QRP +RPQ = 180[Angles in a triangle]

2RQP + 30 = 180

2RQP = 150

RQP =QRP = 75

RQP =RSQ= 75 [ Angles in alternate Segment Theoremstates that angle between chord and tangent is equal to the angle in the alternate segment]

RS II PQ

Therefore RQP = SRQ= 75 [They are alternate angles]

RSQ = SRQ = 75

Therefore QRS is also an isosceles triangle

RSQ + SRQ + RQS = 180 [Angles in a triangle]

75 + 75 + RQS = 180

150 + RQS = 180

RQS = 30

Required Answer: RQS = 30

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in triangle PQR

RPQ= 30

let consider PRQ AND RQP=x

(PQ=PR)

PRQ+QPR+RQP=180 (ASP)

30 + 2x = 180

x= 75

OPR=90 (PR =TANGENT)

ORP=90 and QRP = 75

ORQ=15

SR ll PQ

then,SRQ =RQP

RQP= 75(proved above)=SRQ

SRQ= SRO + ORQ

75= SRO+15

SRO=60= OSR( OR=OS radius of circle)

in triangle OSR

OSR+SRO+ROS=180(ASP)

SOR=60

2 TIMES SOR = SQR

RQS =60/2

=30

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RPQ= 30

let consider PRQ AND RQP=x

(PQ=PR)

PRQ+QPR+RQP=180 (ASP)

30 + 2x = 180

x= 75

OPR=90 (PR =TANGENT)

ORP=90 and QRP = 75

ORQ=15

SR ll PQ

then,SRQ =RQP

RQP= 75(proved above)=SRQ

SRQ= SRO + ORQ

75= SRO+15

SRO=60= OSR( OR=OS radius of circle)

in triangle OSR

OSR+SRO+ROS=180(ASP)

SOR=60

2 TIMES SOR = SQR

RQS =60/2

=30

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