question_answer

If two parallel chords of the a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles \[{{\cos }^{-1}}\left( \frac{1}{7} \right)\]and\[{{\sec }^{-1}}(7)\]at the centre respectively, then the distance between these chords, is : [JEE Online 08-04-2017]

A) \[\frac{8}{\sqrt{7}}\]                                     

B) \[\frac{16}{7}\]

C) \[\frac{4}{\sqrt{7}}\]                                     

D) \[\frac{8}{7}\]

Correct Answer: A

Solution :

 \[\cos 2Q=1/7\] \[=2{{\cos }^{2}}Q-1=1/7\] \[=2{{\cos }^{2}}Q=8/7\] \[{{\cos }^{2}}Q=4/7\] \[=\frac{c{{p}^{2}}}{4}=\frac{4}{7}\]                 \[=Cp=\frac{4}{\sqrt{7}}\] \[\sec 2Q=7\]    \[=\frac{2}{2{{\cos }^{2}}Q-1}=7\] \[=2{{\left( \frac{C{{p}_{2}}}{2} \right)}^{2}}-1=\frac{1}{7}\] \[=2{{\left( \frac{C{{p}_{2}}}{2} \right)}^{2}}=\frac{8}{7}\] \[=\]\[\frac{4}{\sqrt{7}}+\frac{4}{\sqrt{7}}=\frac{8}{\sqrt{7}}\]