O is centre of the circle.
DE is the chord 1 cm away from centre. CH is perpendicular on DE.
∴ CH = 1 cm and DE = 6 cm
FG is the chord 2 cm away from centre. CI is perpendicular on FG.
∴ CI = 2 cm
From centre C, CE and CG are joined.
CE and CG both are radius of the circle.
In ΔCHE we have,
∠CHE = 90° [∵CH is perpendicular on DE]
CH = 1 cm
HE = DE/2 = 3 cm [∵perpendicular drawn from centre bisects chord]
In ΔCGI we have,
∠CIG = 90° [∵CI is perpendicular on FG]
CI = 2 cm
CG = CE = √10 cm
∴ FG = 2 × IG = 2√6 cm [∵perpendicular drawn from centre bisects chord]
∴ The length of the chord is = 2√6 cm
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