Single correct option
In a circle, a chord of length 16 cm is at a distance of 6 cm from the centre. What is the length of a chord at a distance of 8 cm from the centre?
- A. 15 cm
- B. 10 cm
- C. 12 cm
- D. 14 cm
Show answer and solution
Answer: (C) 12 cm
The perpendicular from the centre bisects the chord. For the first chord: r² = 8² + 6² = 100, so r = 10 cm.
For a chord at distance 8 cm: half-length = √(100 − 64) = 6 cm, so the chord is 12 cm.
Tip: Chord = 2√(r² − d²). Recognise the 6-8-10 triple.
For a chord at distance 8 cm: half-length = √(100 − 64) = 6 cm, so the chord is 12 cm.
Tip: Chord = 2√(r² − d²). Recognise the 6-8-10 triple.
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