PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If XR = 12 cm, PQ = x cm, QR = x - 2 cm, then x (in cm) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 10.
RX2 = RQ × PR
⇒ 122 = (x - 2)(x + x - 2)
⇒ 144 = (x - 2)(2x - 2)
⇒ 144 = 2x2 - 2x - 4x + 4
⇒ 144 = 2x2 - 6x + 4
⇒ 2x2 - 6x - 140 = 0
⇒ x2 - 3x - 70 = 0
⇒ x2 - 10x + 7x - 70 = 0
⇒ x(x - 10) + 7(x - 10) = 0
⇒ (x + 7)(x - 10) = 0
⇒ x = 10