Question

6. In a circle of radius 17 cm, two parallel
chords of lengths 30 cm and 16 cm are
drawn. Find the distance between the chords,
if both the chords are :
(i) on the opposite sides of the centre,
(ii) on the same side of the centre.​

Answer 1

Step-by-step explanation:

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>>In a circle of radius 17 cm...

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In a circle of radius 17 cm, two parallel chords of length 30 cm and 16 cm are drawn. Find the distance between the chords, if both chords are on the same sides of the centre.

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Solution

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Let O be the centre of the circle and AB and CD be the two parallel chords of length 30 cm and 16 cm respectively.

Drop OE and OF perpendicular on AB and CD from the centre O

OE⊥AB and OF⊥CD

∴OE bisects AB and OF bisects CD

(pependicular drawn from the centre of a circle to a chord bisects it)

⇒AE=

2

30

=15 cm;CF=

2

16

=8 cm

In triangle △OAE,

OA

2

=OE

2

+AE

2

⇒OE

2

=OA

2

−AE

2

=(17)

2

−(15)

2

=64

∴OE=8 cm

In triangle △OCF,

OC

2

=OF

2

+CF

2

⇒OF

2

=OC

2

−CF

2

=(17)

2

−(8)

2

=225

∴OF=15 cm

The chords are on the same sides of the centre:

∴EF=OF−OE=(15−8)=7 cm

∴ Distance between two parallel chords is 7 cm