Q. 1 G4.3( 12 Votes )

Choose correct alternative answer and fill in the blanks.

The lengths of parallel chords which are on opposite sides of the center of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is .....
A. 2 cm

B. 1 cm

C. 8 cm

D. 7 cm

Answer :


Let, length of AB = 6cm and length of CD = 8cm


Radius of circle = 5cm


OB = OC = 5cm


We know that a perpendicular drawn from the center of a circle on its chord bisects


the chord.


AM = MB = 3cm


Also, CN = ND = 4cm


In ΔOMB,


OB2 = OM2 + MB2


52 = OM2 + 32


OM2 = 25-9


OM2 = 16


OM = 4cm


In ΔONC,


OC2 = ON2 + CN2


52 = ON2 + 42


ON2 = 25-16


ON2 = 9


ON = 3cm


Distance between AB and CD = OM + ON = 4 + 3 = 7cm


Hence the correct option is D.

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