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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.
Solution
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
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