Single correct option
In a circle, a chord of length 30 cm is at a distance of 8 cm from the centre. What is the length of a chord at a distance of 15 cm from the centre?
- A. 16 cm
- B. 14 cm
- C. 18 cm
- D. 12 cm
Show answer and solution
Answer: (A) 16 cm
The perpendicular from the centre bisects a chord.
First chord: half-length 15, distance 8, so r² = 15² + 8² = 289 and r = 17.
Second chord: half-length = √(17² − 15²) = √64 = 8. Full length = 16 cm.
Tip: 8-15-17 is a common triple; distance and half-chord simply swap roles here.
First chord: half-length 15, distance 8, so r² = 15² + 8² = 289 and r = 17.
Second chord: half-length = √(17² − 15²) = √64 = 8. Full length = 16 cm.
Tip: 8-15-17 is a common triple; distance and half-chord simply swap roles here.
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