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

1. 4 cm

2. 5 cm

3. 6 cm

4. 8 cm

The figure is shown below:

Since tangent and radius at point of contact of a circle are perpendicular to each other. Hence,

XAY ⊥ AO

Given XAY || to CD hence,

CD ⊥ AB.

In right angled triangle OEC,

OE = AE - AO = 8 - 5 = 3 cm.

⇒ OC² = OE² + CE² (By pythagoras theorem)
⇒ 5² = 3² + CE²
⇒ CE² = 25 - 9
⇒ CE² = 16
⇒ CE = 4 cm.

Similarly in right angled triangle OED,

⇒ OD² = OE² + ED² (By pythagoras theorem)
⇒ 5² = 3² + ED²
⇒ ED² = 25 - 9
⇒ ED² = 16
⇒ ED = 4 cm.

⇒ CD = CE + ED = 4 + 4 = 8 cm.

Hence, Option 4 is the correct option.