Maharashtra State BoardSSC (English Medium) 9th Standard

Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______. - Geometry

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Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______.

Options

  • 12 cm 

  • 13 cm

  • 14 cm

  • 15 cm

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Solution

Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is 13 cm.

Explanation:

Let the chord be AB = 24 cm

Distance of the chord from the centre O is 5 cm.

AO is the radius of the circle.

Perpendicular from the centre of the circle to the chord bisects the chord. 

So, AC = CB

In ΔAOC, 

OC2 + AC2 = AO2

⇒ 52 + 122 = AO2

⇒ AO2 = 25 + 144 = 169

⇒ AO = 13 cm

Thus, the radius of the circle is 13 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. (iv) | Page 86

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