Two parallel chords of a circle of radius 2 are at a distance √3+1 apart. If the chords subtend at the centre, angles of pi/k and 2pi/k whre k>0 , then the value of [k] is?

Draw the figure. Calculate the value of pi/k and 2pi/k in terms of the length of chords/radius/distance of the chord from the centre. At the center, the sum is 360. use this equality to obtain the value of k by deriving the value of angles formed along the chords and the radii in both the triangles.