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
Let θ=π2k⇒cosθ=x2⇒cos2θ=√3+1−x2⇒2cos2θ−1=√3+1−x2⇒2(x24)−1=√3+1−x2⇒x2+x−3−√3=0⇒x=−1±√1+12+4√32 ...(Root of quadratic equation)=−1±√13+4√32=−1+2√3+12=√3∴ cosθ=√32⇒θ=π6∴Required angle=πk=2θ=π3⇒k=3