Numerical answer
In a circle of radius 10 cm, two parallel chords of lengths 16 cm and 12 cm lie on the same side of the centre. What is the distance (in cm) between the chords?
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Answer: 2
The perpendicular from the centre bisects a chord. Distance of a chord of length L from the centre = √(r² − (L/2)²).
Chord 16: √(100 − 64) = 6.
Chord 12: √(100 − 36) = 8.
Both chords are on the same side of the centre, so the distance between them = 8 − 6 = 2 cm.
(Had they been on opposite sides, the answer would be 6 + 8 = 14.) Read 'same side / opposite sides' carefully.
Chord 16: √(100 − 64) = 6.
Chord 12: √(100 − 36) = 8.
Both chords are on the same side of the centre, so the distance between them = 8 − 6 = 2 cm.
(Had they been on opposite sides, the answer would be 6 + 8 = 14.) Read 'same side / opposite sides' carefully.
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