Question

Find the length of the tangent drawn from a point whose distance whose distance from the centre of a circle is $25cm.$ Given that the radius of the circle is $7cm.$

Answer 1

Let $P$ be the given point, $O$ be the centre of the circle and $PT$ be the length of tangent from $P$.

Then, $OP=25cm$ and $OT=7cm$.
Since tangent to a circle is always perpendicular to the radius through the point of contact.

$\therefore \angle OTP={90}^o$

In right triangle $OTP$, we have
${OP}^2={OT}^2+{PT}^2$

$\Rightarrow {25}^2=7^2+{PT}^2$

$\Rightarrow {PT}^2={25}^2-7^2=(25-7)(25+7)=576$

$\Rightarrow PT=24cm$.

Hence, length of tangent from $P=24cm$.