PQ is a chord of a circle. The tangent XR at point X on the circle intersects the extension of PQ at point R. Given that XR = 12 cm, PQ = x cm, and QR = (x - 2) cm, find the value of x.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10 cm.
PR = x + x - 2 = 2x - 2 cm
PR/RX = RX/RQ
⇒ RX2 = PR × RQ
⇒ 122 = (x - 2)(2x - 2)
⇒ 144 = 2x2 - 6x + 4
⇒ 2x2 - 6x - 140 = 0
⇒ (x - 10)(x + 7) = 0
⇒ x = 10 or - 7 [Length can't be negative]
Hence, the value of x is 10 cm.