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Two parallel chords of a circle of radius 2 units are at a distance 3+1 units apart. If the chords subtend at the centre, angles of πk and 2πk, where k>0, then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___


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Solution


Let θ=π2kcosθ=x2cos2θ=3+1x22cos2θ1=3+1x22(x24)1=3+1x2x2+x33=0x=1±1+12+432 ...(Root of quadratic equation)=1±13+432=1+23+12=3 cosθ=32θ=π6Required angle=πk=2θ=π3k=3


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