Question

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

• A. 4 cm
• B. 5 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is D 8 cm

Given-

AB is the diameter of a circle with center O.

CD is a chord and $CD\parallel AXY$ which is a tangent to the circle at A intersecting AB at N.

$AN=8$cm and $OA=OC=5$cm ...((radius)

To find out-

The length of CD

Solution-

The line $AXY\parallel CD$ and $AXY$ is a tangent to the circle at A.

$\therefore AB\perp AXY$ & $CD.$ i.e $\angle OAY={90}^O=\angle OED$

$\therefore \Delta OEC$ is a right angled one with OC as hypotenuse.

$\therefore {CE}^2={OC}^2-{OE}^2$

$⟹CE=\sqrt{5^2-3^2}cm=4$cm.

But $OE\perp CD$ at E from the centre O.

$\therefore CD=2CE⟹CD=2\times 4$cm $=8cm$