PERPENDICULAR M and N on chords AB and CD respectively.Now,ΔOBM ≅ ΔODNHence, OM = ON = 6/2 = 3 cmNow,MB2 + OM2 = OB2⇒ MB2 + 32 = 52⇒ MB2 = 25 - 9 = 16⇒ MB = 4 cmAM = 2MB⇒ 2 × 4⇒ 8 cm∴ The length of each chord is 8 cm.

"> PERPENDICULAR M and N on chords AB and CD respectively.Now,ΔOBM ≅ ΔODNHence, OM = ON = 6/2 = 3 cmNow,MB2 + OM2 = OB2⇒ MB2 + 32 = 52⇒ MB2 = 25 - 9 = 16⇒ MB = 4 cmAM = 2MB⇒ 2 × 4⇒ 8 cm∴ The length of each chord is 8 cm.

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In a circle, two equal and parallel chords are 6 cm apart and they lie on the opposite sides of the centre of the circle, whose radius is 5 cm. The length of each chord (in cm), is:

SRMJEEE Analytical Geometry in SRMJEEE 1 year ago

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GivenDistance between two equal chords = 6 cmRadius of circle = 5 cmCalculationLets draw PERPENDICULAR M and N on chords AB and CD respectively.Now,ΔOBM ≅ ΔODNHence, OM = ON = 6/2 = 3 cmNow,MB2 + OM2 = OB2⇒ MB2 + 32 = 52⇒ MB2 = 25 - 9 = 16⇒ MB = 4 cmAM = 2MB⇒ 2 × 4⇒ 8 cm∴ The length of each chord is 8 cm.

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