If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles

      \small \cos ^{-1}\left ( \frac{1}{7} \right ) and \sec ^{-1} (7)

at the centre respectively, then the distance between these chords, is :

 

  • Option 1)

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

  • Option 2)

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

  • Option 3)

    \frac{8}{7}

  • Option 4)

    \frac{16}{7}

 

Answers (2)

As we learnt in 

Circle -

A circle is the locus of a moving point such that its distance from a fixed point is constant.

- wherein

 

 and using the concept of chords;

cos\theta =\frac{1}{7}

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

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

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

\Rightarrow cos\frac{\theta }{2}=\frac{OA}{r}=\frac{OA}{2}

OA=\frac{4}{\sqrt{7}}; thus distance between them = OA=\frac{8}{\sqrt{7}}

 


Option 1)

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

This option is incorrect

Option 2)

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

This option is correct

Option 3)

\frac{8}{7}

This option is incorrect

Option 4)

\frac{16}{7}

This option is incorrect

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