Circle 5 Question 24

24. 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 π/k and 2πk, where k>0, then the value of [k] is……

(2010)

NOTE [k] denotes the largest integer less than or equal to k]

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Answer:

Correct Answer: 24. 3

Solution:

  1. Let

θ=π2kcosθ=x2

cos2θ=3+1x2

2cos2θ1=3+1x2

2x241=3+1x2

x2+x33=0

x=1±1+12+432

=1±13+432=1+23+12=3

cosθ=32θ=π6

Required angle =πk=2θ=π3

k=3

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