Numerical answer
In a circle of radius 15 cm, two parallel chords of lengths 18 cm and 24 cm lie on the same side of the centre. What is the distance between the chords, in cm?
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Answer: 3
The perpendicular from the centre bisects a chord, so the distance of a chord of length L from the centre is √(r² − (L/2)²).
- Chord 18: √(225 − 81) = 12 cm.
- Chord 24: √(225 − 144) = 9 cm.
Both are on the same side of the centre, so the distance between them is the difference: 12 − 9 = 3 cm. (Had they been on opposite sides, the answer would be 12 + 9 = 21 cm.)
Tip: The longer chord is always closer to the centre — check which perpendicular distance is smaller before subtracting.
- Chord 18: √(225 − 81) = 12 cm.
- Chord 24: √(225 − 144) = 9 cm.
Both are on the same side of the centre, so the distance between them is the difference: 12 − 9 = 3 cm. (Had they been on opposite sides, the answer would be 12 + 9 = 21 cm.)
Tip: The longer chord is always closer to the centre — check which perpendicular distance is smaller before subtracting.
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