Let C be a circle given by the equation x^2 + y^2 = 25 . A chord AB of the circle lies on the line 3x + 4y - 15 = 0 . A second chord CD is parallel to AB , lies on the same side of the centre as AB , and is shorter in length than AB . If the distance between the two chords is 1 unit, then the length of the chord CD (in units) is

Step-by-step solution

The radius of the circle x^2 + y^2 = 25 is r = 5 . The perpendicular distance of the chord AB from the centre (0, 0) is: d₁ = |3(0) + 4(0) - 15| 3^2 + 4^2 = 15 5 = 3 Since the chord CD is parallel to AB and lies on the same side of the centre, its distance from the centre can be either d₁ - 1 = 2 or d₁ + 1 = 4 . We are given that CD is shorter than AB . A shorter chord is further from the centre, so its distance from the centre must be greater than d₁ . Thus, the distance of CD from the centre is d₂ = 4 . The lengt