Numerical answer
Two parallel chords of lengths 16 cm and 12 cm are drawn in a circle of radius 10 cm, on opposite sides of the centre. What is the distance (in cm) between the chords?
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Answer: 14
The perpendicular from the centre bisects a chord.
Chord 16: half-length 8, distance from centre = √(10² − 8²) = 6.
Chord 12: half-length 6, distance from centre = √(10² − 6²) = 8.
On opposite sides of the centre, the distance between them = 6 + 8 = 14 cm. (Had they been on the same side, it would be 8 − 6 = 2 cm.)
Chord 16: half-length 8, distance from centre = √(10² − 8²) = 6.
Chord 12: half-length 6, distance from centre = √(10² − 6²) = 8.
On opposite sides of the centre, the distance between them = 6 + 8 = 14 cm. (Had they been on the same side, it would be 8 − 6 = 2 cm.)
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