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 $XY$ 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

We have , $AN=8$ cm

So, $ON=AN-OA$

$\Rightarrow ON=8-5$

$\Rightarrow ON=3$ cm

Since $ON$ is perpendicular to the chord $CD$,

So, In $△OCM$

By Pythagoras theorem, we get

$CN=\sqrt{(OC{)}^2-(ON{)}^2}$

$\Rightarrow CN=\sqrt{(5{)}^2-(3{)}^2}$

$\Rightarrow CN=\sqrt{(25-9)}$

$\Rightarrow CN=\sqrt{16}$

$\Rightarrow CN=4$

Hence, $CD=2\times CN$

$=2\times 4$

$=8$ cm