Question

In following fig., chords PQ and RS of a circle intersect at T. If RS = 18cm, ST = 6cm and PT = 18cm, find the length of TQ. 

Answer 1

Let TQ = x cm 

In Δ PTR and Δ STQ 

∠ TPR = ∠ TSQ   (angles in the same segment) 

∠ PTR = ∠ STQ   (vertically opposite L's) 

∴ ∠ PTR = ∠ STQ   {AA corollary) 

`"PT"/"ST" = "TR"/"TQ"`  (similar sides of similar triangles) 

`18/6 = 12/"x"`

= x = 4

⇒ TQ = 4 cm