Question

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

• A. $\frac{4}{\sqrt{7}}$
• B. $\frac{8}{\sqrt{7}}$
• C. $\frac{8}{7}$
• D. $\frac{16}{7}$

Answer 1

Answer: (B)

$cos2Q=1/7=2co{s}^{2}Q-1=1/7$
$=2co{s}^{2}Q=8/7$
$=cos2Q=4/7$
$=\frac{c{p}^2}{4}=\frac{4}{7}$
$=Cp=\frac{4}{\sqrt{7}}$
$sec2Q=7=\frac{1}{2co{s}^{2}Q1}=7$
$=2{\left(\frac{C{p}_2}{2}\right)}^2-1=\frac{1}{7}$
$=2{\left(\frac{C{p}_2}{2}\right)}^2=\frac{8}{7}$
$=C{p}_2=\frac{4}{\sqrt{7}}$
$\frac{4}{\sqrt{7}}+\frac{4}{\sqrt{7}}=\frac{8}{\sqrt{7}}$