Question

If two parallel chords of a circle, having diameter $4units$, 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. $\frac{8}{\sqrt{7}}$
• B. $\frac{4}{\sqrt{7}}$
• C. $\frac{8}{7}$
• D. $\frac{16}{7}$

Answer 1

The correct option is A $\frac{8}{\sqrt{7}}$

$cos2Q=1/7$
$=2co{s}^{2}Q-1=1/7$
$=2co{s}^{2}Q=8/7$
$co{s}^{2}Q=\frac{4}{7}$
$=\frac{c{p}_1^2}{4}=\frac{4}{7}$
$=c{p}_1=\frac{4}{\sqrt{7}}$
$sec2Q=7=\frac{1}{2co{s}^{2}Q-1}=7$
$=2{\left(\frac{c{p}_2}{2}\right)}^2-1=\frac{1}{7}$
$=2{\left(\frac{c{p}_2}{2}\right)}^2=\frac{8}{7}$

$=c{p}_2=\frac{4}{\sqrt{7}}$

$=\frac{4}{\sqrt{7}}+\frac{4}{\sqrt{7}}=\frac{8}{\sqrt{7}}$