PQR is inscribed in a circle. The bisector of P cuts QR at S and the circle at T. If PR = 5 cm, PS = 6 cm and ST= 4 cm. then the length (in cm) of PQ is:
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Let PS be x cm, then QS = (15 – x) cm
PS = PU, QS = QT, RT = RU [tangents]
⇒ QT = (15 – x) cm
⇒ RT = 10 – (15 – x) = x – 5
⇒ RU = (x – 5)
⇒ PU = 12 – x + 5 = 17 – x
⇒ 17 – x = x
⇒ 2x = 17
⇒ x = 17/2
⇒ x = 8.5 cm
⇒ PS = 8.5
⇒ QT = 15 – 8.5 = 6.5
⇒ RU = 8.5 – 5 = 3.5
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