Two parallel chords of a circle of radius unity which are on the same side of the centre subtend angles 75° and 165° at the centre as shown in the figure. The distance between the chords is

Engineering

Mathematics

A Circle

compound angle Formulae

Definition of Trigonometric Ratio

Question

Two parallel chords of a circle of radius unity which are on the same side of the centre subtend angles 75° and 165° at the centre as shown in the figure. The distance between the chords is

$\frac{\sqrt{6 - 2 \sqrt{2}}}{2}$

$\frac{\sqrt{6 - 4 \sqrt{2}}}{2}$

$\frac{\sqrt{6 - 3 \sqrt{2}}}{2}$

$\frac{\sqrt{6 - \sqrt{2}}}{2}$

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Distance = cos $\frac{75 °}{2}$ – cos $\frac{165 °}{2}$ = 2 sin 60° sin $(22 \frac{1}{2}) °$

= $2 \times \frac{\sqrt{3}}{2} \times \frac{\sqrt{2 - \sqrt{2}}}{2}$ = $\frac{\sqrt{6 - 3 \sqrt{2}}}{2}$