Question

. Determine the length of the chord which
is at a distance of 12 cm from the centre
of a circle of radius 13 cm.​

Answer 1

★ Answer :-

• → The length of the chord is 10 cm

★ GivEn :-

• The distance of the chord from centre is 12 cm
• The radius us 13 cm.

★ To Find :-

• The length of the chord

★ Solution :-

Let the length of radius be OB which is 13 cm.

And the distance between chord and centre of the circle be OA which is 12 cm.

And let the chord be BC cm.

Therefore, OA is perpendicular on BC.

So, ∠OAB = 90°

△OAB is right angle triangle.

Now we know that, in a right angle triangle,

$\boxed{ \sf{Hypotenuse^{2} = Base^{2} + Height^{2} }}$

$\implies \sf \: {13}^{2} = {x}^{2} + {12}^{2}$

$\implies \sf \: {x}^{2} = {13}^{2} - {12}^{2}$

$\implies \sf \: {x}^{2} = 169 - 144$

$\implies \sf \: {x}^{2} = 25$

$\implies \boxed{\sf \: x = 5}$

The length of the chord is 2x = 10 cm.

Answer 2

Answer:

the length of the chord is =(√13^2-12^2)×2=5×2=10cm.