Question

Ar one end A of diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle
Find the length of the chord CD which is at a distance 8 cm from A and parallel to XY​

Answer 1

Answer: 8 cm

Step-by-step explanation: =OAY=90°

As sum of cointerior angle is 180°.

Therefore,

angleOAY+angleOED=180°

= angleOED=90°

AE=8cm(From fig.)

Now in  triangle OEC, by pythagoras theorem,

OC  

2

=OE  

2

+EC  

2

 

=EC  

2

=OC  

2

−OE  

2

 

-EC  

2

=(5)  

2

−(3)  

2

 

⇒EC=  

25−9

​  

=4

Therefore,

Length of chord CD=2×CE(perpendicular from centre to the chord bisects the chord)

⇒CD=2×4=8cm

Hence the length of the chord CD is 8cm