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?

Answer :

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


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