Within a circle, two parallel chords are positioned such that the center lies between them if the distance between these chords is 14 cm, and the length of one chord is 12 cm having radius of 10 cm, what is the length of the other chord?
Show answer & explanation
Correct answer: B
Explanation
Radius = 10 cm
Length of the first chord = 12 cm
Distance of the first chord from the center = √(10² − (12/2)²)
= √(100 − 6²)
= √64
= 8 cm
The distance between the two chords is 14 cm, and the center lies between them.
Therefore, the distance of the second chord from the center = 14 − 8
= 6 cm
Length of the second chord = 2 × √(10² − 6²)
= 2 × √(100 − 36)
= 2 × 8
= 16 cm