Question

a CHORD of length 16 cm is at the distance 6 cm from the centre of the circle.find the length of the chord of the same circle which is at a distance 8 cm from the centre.​

Answer 1

Step-by-step explanation:

AB is the chord of circle with centre O and

OA is the radius of the circle and OM⊥AB

AB=16cm,OM=6cm

OM⊥AB=1/2×16 = 8 cm

Now right △OAM,

OA

2

=AM

2

+OM

2

(by Pythagoras Axiom)

=(8)

2

+(6)

2

64+36=100=(10)

2

Now CD is another chord of the same circle

ON⊥CD and OC is the radius

Now right △ONC,

OC

2

=ON

2

+NC

2

(by Pythagoras Axiom)

(10)

2

=(8)

2

+(NC)

2

100=64+(NC)

2

(NC)

2

=100−64=36=(6)

2

NC=6

But ON⊥AB

N is the mid-point of CD

CD=2NC=2×6 = 12 cm