Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Two parallel chords of a circle of radius 2 are at a distance 
apart. If the chords subtend at the center, angles of 
and 
, where k > 0, then the value of [k] is
Text Solution
Verified by ExpertsThe correct answer is:
3
(3)Since distance between parallel chords is greater than radius, therefore both chords lie on opposite side of centre.
2 cos 
+ 2 cos 
= 
+ 1
Let 
= θ 
∴ 2 cos θ + 2 cos 2 θ = 
+ 1 ⇒ 2 cos θ + 2 (2 cos 2 θ – 1) = 
+ 1
⇒ 4 cos 2 θ + 2 cos θ – (3 + 
) = 0
∴ cos θ = 
= 
= 
= 
⇒ cos 
= 
, 
Rejected
⇒ 
= 
⇒ k = 3 ⇒ [k] = 3
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