In a circle of radius 5 centimetres, two parallel chords of lengths 6 and 8 centimetres are drawn on either side of a diameter. What is the distance between them? If parallel chords of these lengths are drawn on the same side of a diameter, what would be the distance between them?

When chords are drawn on either side of diameter.

O is the centre of the circle and IJ is the diameter.

CD and EF are two parallel chord on either side of the diameter.

CD = 6 cm and EF = 8 cm

OH is the perpendicular drawn on CD from centre.

OG is the perpendicular drawn on EF from centre.

In ΔOGE we have,

∠OGE = 90° [∵ OG is perpendicular on EF]

EG = EF/2 = 4 cm [∵perpendicular drawn from centre bisects chord]

OE = 5 cm [radius]

In ΔOHC we have,

∠OHC = 90° [∵ OH is perpendicular on CD]

HC = CD/2 = 3 cm [∵perpendicular drawn from centre bisects chord]

OC = 5 cm [radius]

∴ Distance between the chords = HG = OH + OG = 4 + 3 = 7 cm

When the chords are drawn on same side of diameter:

O is the centre of the circle and IJ is the diameter.

CD and EF are two parallel chords on same side of the diameter.

CD = 6 cm and EF = 8 cm

OH is the perpendicular drawn on CD from centre.

OG is the perpendicular drawn on EF from centre.

In ΔOGE we have,

∠OGE = 90° [∵ OG is perpendicular on EF]

EG = EF/2 = 4 cm [∵perpendicular drawn from centre bisects chord]

OE = 5 cm [radius]

In ΔOHC we have,

∠OHC = 90° [∵ OH is perpendicular on CD]

HC = CD/2 = 3 cm [∵perpendicular drawn from centre bisects chord]

OC = 5 cm [radius]

∴ Distance between the chords = HG = OH – OG = 4 – 3 = 1 cm