If two parallel chords of a circle, having diameter $4\ units$, lie on the opposite sides of the centre and subtend angles $\cos^{-1}\left(\displaystyle\frac{1}{7}\right)$ and $\sec^{-1}(7)$ at the centre respectively, then the distance between these chords, is:
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$\displaystyle\frac{8}{\sqrt{7}}$
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$\displaystyle\frac{4}{\sqrt{7}}$
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$\displaystyle\frac{8}{7}$
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$\displaystyle\frac{16}{7}$
A
Correct answer
Explanation
Radius r = 2. Angles are cos^-1(1/7) and sec^-1(7) = cos^-1(1/7). Both chords subtend the same angle at the center. Distance from center to each chord = r * cos(theta/2). Using half-angle formulas, the distance is 2 * sqrt((1+1/7)/2) = 2 * sqrt(4/7) = 4/sqrt(7). Since they are on opposite sides, total distance = 8/sqrt(7).