Question

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm.

Answer 1

Given : A chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm.

 

Let the distance of the chord from the centre ,  OC = 5 cm and  Radius of the circle,  OA = 10 cm  

 

 

In ΔOCA,  by using Pythagoras theorem

OA² = AC² + OC²

10² = AC² + 5²

100 = AC² + 25

AC² = 100 – 25

AC²  = 75

AC = √75

AC = 8.66 cm

We know that,the perpendicular from centre to chord bisects the chord.

∴ AC = BC = 8.66 cm

Then,

Chord AB = AC + BC  

Chord AB = 8.66 + 8.66

Chord AB = 17.32 cm

 Hence,  the length of a chord is 17.32 cm

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Answer:-

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Given :

A chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm.

 

Let the distance of the chord from the centre ,  OC = 5 cm and  Radius of the circle,  OA = 10 cm  

 

 

In ΔOCA,  by using Pythagoras theorem

OA² = AC² + OC²

10² = AC² + 5²

100 = AC² + 25

AC² = 100 – 25

AC²  = 75

AC = √75

AC = 8.66 cm

We know that,the perpendicular from centre to chord bisects the chord.

∴ AC = BC = 8.66 cm

Then,

Chord AB = AC + BC  

Chord AB = 8.66 + 8.66

Chord AB = 17.32 cm

 Hence,  the length of a chord is 17.32 cm

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