Maharashtra State BoardSSC (English Medium) 9th Standard

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is ______. - Geometry

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MCQ
Fill in the Blanks

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is ______.

Options

  • 16 cm

  • 8 cm

  • 12 cm

  • 32 cm

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Solution

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is 16 cm.

Explanation:

Let the chord be AB. 
O be the centre and OC be the perpendicular drawn from the centre of the circle to the chord AB. 
Perpendicular drawn from the centre of the circle to the chord bisects the chord. 
AC = CB
OA is the radius =  10 cm
In Δ OAC,

OC2 + AC2 = OA2

⇒ 62 + AC2 = 102

⇒ 36 + AC2 = 100

⇒ AC2 = 64

⇒ AC = 8 cm

AC = CB = 8 cm

AB = AC + CB = 8 + 8 = 16 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. (i) | Page 86

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