A variable triangle ABC is inscribed in a circle of diameter in a circle of diameter x units. At a particular instant, the rate of change in side a is $\large\frac{x}{2}$ times the rate of change in its opposite angle A. Then A=

Question

$$\begin {array} {1 1} (1)\;\frac{\pi}{2} & \quad (2)\; \frac{\pi}{3} \\ (3)\;\frac{\pi}{4} & \quad (4)\;\frac{\pi}{6} \end {array}$$