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 k and 2 k , where k0 , then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k ]

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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 k and 2 k , where k>0 , then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k ]

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Let = 2 k aligned & = x 2 & 2 = 3 +1-x 2 & 2 ^2 -1= 3 +1-x 2 & 2 ( x^2 4 )-1= 3 +1-x 2 & x^2+x-3- 3 =0 & x= -1 1+12+4 3 2 & = -1 13+4 3 2 & = -1+2 3 +1 2 = 3 & = 3 2 = 6 & Required angle = k =2 = 3 & k=3 & aligned

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 k and 2 k , where k>0 , then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k ]

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