Question

tangent PQ and PR are drawn from an external point P to a circle with Centre O and angle rpq = 20 °.A chord RS is drawn parallel to the tangent PQ. find angle RQS

Answer 1

Step-by-step explanation:

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