What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of 45\(^\circ\) ?

Explanation

The length of a chord subtending angle \theta is 2r\sin(\theta/2). For a unit circle (r=1) and \theta = 45^\circ, length = 2\sin(22.5^\circ) = 2 \times \sqrt{\frac{1-\cos 45^\circ}{2}} = 2 \times \frac{\sqrt{2-\sqrt{2}}}{2} = \sqrt{2-\sqrt{2}}.

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