Q. 2

# 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] In ΔOHC we have,

OHC = 90° [ OH is perpendicular on CD]

HC = CD/2 = 3 cm [perpendicular drawn from centre bisects chord] 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] In ΔOHC we have,

OHC = 90° [ OH is perpendicular on CD]

HC = CD/2 = 3 cm [perpendicular drawn from centre bisects chord] Distance between the chords = HG = OH – OG = 4 – 3 = 1 cm

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