Question

In a circle of radius 17cm calculate the length of a chord which is 8 cm from the center

Answer 1

$<b >$ SOLUTION :-

$<u >$ Let a circle be given with centre O. Let AB be the chord.

Given, radius, OA = 17 cm
OD perpendicular to AB = 8 cm

Now Applying PYTHAGORAS THEOREM in triangle OAD,

OA^2 = OD^2 + AD^2
=> 17^2 = 8^2 + AD^2
=> AD^2 = 289 - 64
=> AD^2 = 225
=> AD = 15 cm

We know that a perpendicular drawn from the centre to a chord bisects the chord. Here, OD bisects AB.

Therefore, AB = 2 × 15 = 30 cm

Hence, the length of the chord is 30 cm.

Hope you got it!

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Answer 2

Let a circle be given with centre O. Let AB be the chord. 

Given, radius, OA = 17 cm 
OD perpendicular to AB = 8 cm 

Now Applying PYTHAGORAS THEOREM in triangle OAD, 

OA^2 = OD^2 + AD^2
=> 17^2 = 8^2 + AD^2
=> AD^2 = 289 - 64
=> AD^2 = 225
=> AD = 15 cm

We know that a perpendicular drawn from the centre to a chord bisects the chord. Here, OD bisects AB. 

Therefore, AB = 2 × 15 = 30 cm

Hence, the length of the chord is 30 cm. 


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