In the given figure, QRTS is a cyclic quadrilateral. If PT = 5cm,

In the given figure, QRTS is a cyclic quadrilateral. If PT = 5cm, SQ = 4cm, PS = 6cm and ∠PQR = 63°, then what is the value (in cm) of TR?

A. 3

B. 7

C. 9

D. 15

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Given: QSTR is a cyclic quadrilateral

Sum of the opposite angles = 180

So, ∠STR = 117°

Also, ∠PTS = 180° - ∠STR

⇒ ∠PTS = 63°

And, ∠PST = ∠TRQ (∵ ∠PST + ∠TSQ = ∠TRQ + ∠TSQ = 180°)

So, PTS and PQR are similar triangles

Hence, PT/PQ = PS/PR

⇒ 5/10 = 6/PR

⇒ PR = 12 cm

⇒ PT + TR = 12 cm

∴ TR = 12 – 5 = 7