Two parallel chords of a circle of radius 2 units are `(sqrt3+1)` units apart. If these chords subtend, at the centre, angles of `90^@ /k" and "180^@/k`, where kgt0, then find the value of k.

Explanation

If the figure, two parallel chords AB and CD are at distance `sqrt3+1` units.
Chord AB and CD subtend a angles `90^(@)/k" and "180^@/k` at the centre O, respectively.
`:. angleAOP=90^@/k" and " angleCOQ=180^@/k`
In triangle AOP, `Op=2 cos(90^(@))/k`
In triangle `COQ, OQ=2cos(180^(@))/k`
Now, `PQ+OQ=2cos (90^(@))/k+2cos(180^(@))/k`
`:. 2cos(90^(@))/k+cos180^@/k=sqrt3/2+1/2`
Clearly, value of k is 3.