Numerical answer
In a circle, a chord of length 48 cm is at a distance of 7 cm from the centre. What is the length (in cm) of another chord of the same circle that is at a distance of 24 cm from the centre?
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Answer: 14
The perpendicular from the centre bisects a chord. For the first chord, half-length = 24, distance = 7, so radius = √(24² + 7²) = √625 = 25 cm.
For the second chord at distance 24: half-length = √(25² − 24²) = √49 = 7, so the chord is 14 cm.
Tip: Recognise the 7-24-25 triple — both chords use the same right triangle with legs swapped.
For the second chord at distance 24: half-length = √(25² − 24²) = √49 = 7, so the chord is 14 cm.
Tip: Recognise the 7-24-25 triple — both chords use the same right triangle with legs swapped.
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