Maharashtra State BoardSSC (English Medium) 9th Standard

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is ______. - Geometry

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MCQ
Fill in the Blanks

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

Options

  • 2 cm

  • 1 cm 

  • 8 cm

  • 7 cm

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Solution

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is 7 cm.

Explanation:

Let the chords be AB = 6 cm and CD = 8 cm

O be the centre with OA = OC = 5 cm as radius.

OE ⊥  AB and OF ⊥  CD.
In ΔAEO,

AE2 + EO2 = AO2

⇒ 32 + EO2 = 52

⇒ 9 + EO2 = 25

⇒ EO2 = 16

⇒ EO = 4 cm

In ΔOFC,

OF2 + CF2 = OC2

⇒ OF2 + 42 = 52

⇒ OF2 + 16 = 25

⇒ OF2 = 9

⇒ OF = 3 cm

Thus, the distance between the two chords is EO + OF = 4 + 3 cm = 7 cm.

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Chapter 6: Circle - Problem Set 6 [Page 86]

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Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 6 Circle
Problem Set 6 | Q 1. (vii) | Page 86

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