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 π and k 2 π , where k 0 , then the value of [ k ] is [Note : [ k ] d

Question

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

TestHub · Accepted Answer

Let θ = 2 k π ​ ​ cos θ = 2 x ​ ⇒ cos 2 θ = 2 3 ​ + 1 − x ​ ⇒ 2 cos 2 θ − 1 = 2 3 ​ + 1 − x ​ ⇒ 2 ( 4 x 2 ​ ) − 1 = 2 3 ​ + 1 − x ​ ⇒ x 2 + x − 3 − 3 ​ = 0 ⇒ x = 2 − 1 ± 1 + 12 + 4 3 ​ ​ ​ = 2 − 1 ± 13 + 4 3 ​ ​ ​ = 2 − 1 + 2 3 ​ + 1 ​ = 3 ​ ∴ cos θ = 2 3 ​ ​ ⇒ θ = 6 π ​ ∴ Required angle = k π ​ = 2 θ = 3 π ​ ⇒ k = 3 ​

Mathematics - Circle Question with Solution | TestHub

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