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.

Correct option is D

Given:

A chord PQ as shown is extended to R
From R tangent is drawn at X
XR=12cm, PQ= x cm, QR = x-2 cm
Formula Used:
​$$\frac{PR}{RX} = \frac{RX}{RQ} \\RX^2 = PR \times RQ$$​​
Solution:
PR = PQ+ QR = x+ x-2
RQ = x-2
​$$12^2= (x-2)(2x-2)\\144= 2x^2-2x-4x+4\\2x^2-6x-140=0\\x=10 or x= -7\\$$

Alternate Method:

PR = x + x - 2 = 2x - 2

RQ = x - 2

12$$^2$$​ = (x - 2) (2x - 2)

144 = (x - 2) (2x - 2)

From that if you put x = 10

Then , 

We get , 18 × 8 = 144 cm