Question

In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T. 

(i) Prove ∆ TPS ~ ∆ TRQ. 

(ii) Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm. 

(iii) Find area of quadrilateral PQRS if area of ∆ PTS = 27cm² 

Answer 1

(i) In ∆ TPS and ∆ TRQ

[∵ exterior angle of cyclic quadrilateral is equal to the interior opposite angle] 

∠ T = ∠ T (common) 

∴ ∆ TPS ~ ∆ TRQ (By AA)

(ii) In similar triangles ∆ TPS and ∆ TRQ

(iii)