\( \mathrm{P} \) Two parallel chords of a circle of radius 2 are at...

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\( \mathrm{P} \)
Two parallel chords of a circle of radius 2 are at a distance \( \sqrt{3}+1 \) apart. If the chords subtend at the
W center, angles of \( \frac{\pi}{\mathrm{k}} \) and \( \frac{2 \pi}{\mathrm{k}} \) where \( \mathrm{k}0 \), then the value of \( [\mathrm{k}] \) is
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