If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos−117 and sec−17 at the centre respectively, then the distance between these chords, is

2θ=cos−117⇒cos2θ=17⇒2cos2θ−1=17⇒cos2θ=47⇒cosθ=27But cosθ=x2⇒27=x2⇒x=47Distance b/w the chords =2x=87

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos−117 and sec−17 at the centre respectively, then the distance between these chords, is

2θ=cos−117⇒cos2θ=17⇒2cos2θ−1=17⇒cos2θ=47⇒cosθ=27But cosθ=x2⇒27=x2⇒x=47Distance b/w the chords =2x=87

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If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles $\cos^{- 1} (\frac{1}{7}) a n d \sec^{- 1} (7)$ at the centre respectively, then the distance between these chords, is

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$\frac{16}{7}$

$\frac{8}{\sqrt{7}}$

$\frac{8}{7}$

$\frac{4}{\sqrt{7}}$

answer is B.

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Detailed Solution

$2 θ = \cos^{- 1} (\frac{1}{7})$

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

$\Rightarrow \cos^{2} θ = \frac{4}{7}$

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

But $\cos θ = \frac{x}{2} \Rightarrow \frac{2}{\sqrt{7}} = \frac{x}{2}$

$\Rightarrow x = \frac{4}{\sqrt{7}}$

Distance b/w the chords $= 2 x = \frac{8}{\sqrt{7}}$

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