The distance between the two parallel lines is 1 unit. A point ' \( A \) ' is chosen to lie betw...

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The distance between the two parallel lines is 1 unit. A point ' \( A \) ' is chosen to lie between the lines at a distance ' \( d \) ' from one of them. Triangle \( A B C \) is equilateral with \( B \) on one line and \( C \) on the other parallel line. The length of the side of the equilateral triangle is
(1) \( \frac{2}{3} \sqrt{d^{2}+d+1} \)
(2) \( 2 \sqrt{\frac{d^{2}-d+1}{3}} \)
(3) \( 2 \sqrt{d^{2}-d+1} \)
(4) \( \sqrt{d^{2}-d+1} \)
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