Consider a string $\text{P}$ of length $l$ that is laid out as a straight-line segment. Another string $\text{K}$ is laid out as a semicircular arc with string $\text{P}$ as its diameter, as represented in Figure $\text{(i)}.$ When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string $\text{K}$ forms a full circle with the shortened string $\text{P}$ as its diameter, as represented in Figure $\text{(ii)}.$ The value of $x / l$ is $\_\_\_\_$
- $\pi$
- $\dfrac{\pi-1}{2 \pi}$
- $\dfrac{\pi}{2(\pi-1)}$
- $\dfrac{\pi}{\pi-1}$
