Problem

Two parallel chords are drawn on the same side of the centre of a circle of radius

R

. It is found that they subtend an angle of

\theta

and

2\theta

at the centre of the circle. The perpendicular distance between the chords is a.

2R \sin \frac{3\theta}{2} \sin \frac{\theta}{2}

\left(1 - \cos \frac{\theta}{2}\right) \left(1 + 2 \cos \frac{\theta}{2}\right) R

\left(1 + \cos \frac{\theta}{2}\right) \left(1 - 2 \cos \frac{\theta}{2}\right) R

2R \sin \frac{3\theta}{4} \sin \frac{\theta}{4}