Question

108°

6) What is the length of the chord, if radius of the circle is 5 cm and distance of the chord from the centre is 3 cm ? *

1 point

2 cm

4 cm

8 cm

16 cm​

Answer 1

Given:-

• Radius of the circle is 5 cm and distance of the chord from the centre is 3 cm.

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To find:-

• Length of the chord.

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Solution:-

★ In this question we have given that the radius of the circle is 5 cm and distance of the chord from the centre is 3 cm. We have to find out the length of the chord. Let's do it.

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By Pythagoras Theorem:-

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⇢ OA² = OM² + AM²

• The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

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⇢ AM² = 5² - 3²

⇢ AM = √16

⇢ AM = 4 cm

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Therefore,

⇢ AB = 2AM

⇢ AB = 2 × 4

⇢ AB = 8 cm

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Hence,

• The length of the chord is 8 cm.

Answer 2

A N S W E R :

• The length of the chord is 8 cm.

Given :

• Radius of the circle is 5 cm and distance of the chord from the centre is 3 cm

To find :

• Find the length of the chord ?

Solution :

• Radius of circle is 5 cm

Therefore,

• OA = 5

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• Prependicular drawn to the chord from the centre bisects the chord

So,

• AM = MB

∆OMA is right angled triangle at M ∠OMA = 90°

As we know that,

By applying Pythagoras Therom :

★ OA² = OM² + MA²

=> MA = √OA² - OM²

=> MA = √5² - 3²

=> MA = √16

=> MA = 4

Therefore,

• Length of chord AB = 2MA

Hence,

• The length of the chord is 8 cm.