Answer :

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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