If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos - 1 ⁡ 1 7 and sec - 1 ⁡ 7 at the center respectively, then the distance between these chords is:

Step-by-step solution

Given condition, ∴   cos ⁡ 2 θ = 1 7 ⇒ 2 cos 2 θ - 1 = 1 7 ⇒ 2 cos 2 ⁡ θ = 8 7 ⇒ cos θ = 2 7 Then, C P 1 = r cos θ = 4 7 Since, cos − 1 1 7 = sec − 1 7 , hence both the chords are at equal distance from center of the circle. Hence, the distance between the chords = 2 × 4 7 = 8 7 .