Question

The length of the tangent drawn from a point $8$ cm away from the centre of a circle of radius $6$ cm is:

• A. $\sqrt{7}$ cm
• B. $2\sqrt{7}$ cm
• C. $10$ cm
• D. $5$ cm

Answer 1

The correct option is B $2\sqrt{7}$ cm

Let $O$ be the centre of the circle. $OA$ is the radius of the circle and $OP$ is $8$ cm

According to question, we have

$\angle OAP={90}^0$

So,cby Pythagoras theorem,cwe get

$O{P}^2=O{A}^2+A{P}^2$

$\Rightarrow A{P}^2=O{P}^2-O{A}^2$

$\Rightarrow A{P}^2=8^2-6^2$

$\Rightarrow A{P}^2=64-36$

$\Rightarrow A{P}^2=28$

$\Rightarrow AP=2\sqrt{7}$ cm