Question

Two sides PQ and SR of a cyclic quadrilateral PQRS are extended to meet at the point T. O is the centre of circle. If ​

Answer 1

Step-by-step explanation:

We know that

TR−TS=TQ.TP

⇒

TP

TR

=

TS

TQ

Also ∠RTQ=∠STP

⇒△TPS∼△TRQ

ii) So,

TR

TP

=

RQ

SP

⇒

6

18

=

4

SP

⇒SP=12 cm

iii)

ar(△QTR)

ar(△PTS)

=(

TR

TP

)

2

=(

6

18

)

2

=9

⇒

ar(△QTR)

27

=9⇒ar(△QTR)=3 cm

2

ar(PQRS)=ar(△PTS)−ar(△QTR)=27−3=24 cm

2