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)

$cos 2Q = 1/7 = 2cos^{2}Q - 1 = 1/7$
$= 2 cos^{2}Q = 8/7$
$= cos2Q = 4/7$
$= \frac{cp^{2}}{4} = \frac{4}{7}$
$= Cp = \frac{4}{\sqrt{7}}$
$sec2Q = 7 = \frac{1}{2 cos^{2} Q 1} = 7$
$= 2\left(\frac{Cp_{2}}{2}\right)^{2}-1 = \frac{1}{7}$
$= 2\left(\frac{Cp_{2}}{2}\right)^{2} = \frac{8}{7}$
$= Cp_{2} = \frac{4}{\sqrt{7}}$
$\frac{4}{\sqrt{7}}+\frac{4}{\sqrt{7}} = \frac{8}{\sqrt{7}}$