If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and…

Given condition, 

$\therefore \cos 2\theta =\frac{1}{7}$ $\Rightarrow 2{\cos }^2\theta -1=\frac{1}{7}$

$\Rightarrow 2{\cos }^2\theta =\frac{8}{7}$

$\Rightarrow \cos \theta =\frac{2}{\sqrt{7}}$

Then, $C{P}_1=r\cos \theta =\frac{4}{\sqrt{7}}$

Since, ${\cos }^{-1}\frac{1}{7}={\sec }^{-1}7$, hence both the chords are at equal distance from center of the circle.

Hence, the distance between the chords $=2\times \frac{4}{\sqrt{7}}=\frac{8}{\sqrt{7}}.$