Maharashtra State BoardSSC (English Medium) 8th Standard
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C is the Centre of the Circle Whose Radius is 10 Cm. Find the Distance of the Chord from the Centre If the Length of the Chord is 12 Cm. - Mathematics

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Sum

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.

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Solution

C is the centre of the circle.
Radius = 10 cm
Let the chord be AB. 
Distance of the centre to the chord = AB.
CD is perpendiculaar to the chord AB. 
Perpendicular drawn from the centre of the circle to the chord bisects the chord. 

AD = `"AB"/2 = 12/2` = 6 cm

In Δ ACD,
We apply the Pythagoras theorem

CD² + AD² = AC²

⇒ CD² + 6² = 10²

⇒ CD² + 36² = 100

⇒ CD² = 64

⇒ CD = 8 cm 

Thus, distance of the chord from the centre is 8 cm. 

Concept: Properties of Chord of a Circle
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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 17 Circle : Chord and Arc
Practice Set 17.1 | Q 4 | Page 116
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