Question

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

Answer 1

Answer:

A chord CD is drawn which is parallel to XY and at a distance of 8cm from A.

As we know that tangent at any point of a circle is perpendicular to the radius through the point of contact.

∴∠OAY=90°

As sum of cointerior angle is 180°.

Therefore,

∠OAY+∠OED=180°

⇒∠OED=90°

AE=8cm(From fig.)

Now in △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